{"id":39544,"date":"2022-04-03T17:01:06","date_gmt":"2022-04-03T11:31:06","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=39544"},"modified":"2022-04-07T11:27:52","modified_gmt":"2022-04-07T05:57:52","slug":"big-ideas-math-algebra-2-answers-chapter-9","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-9\/","title":{"rendered":"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions"},"content":{"rendered":"<p>Are you struggling to solve the trigonometric ratios and functions in homework and assignments? Then, check out this <strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers\/\">Big Ideas Math Algebra 2 Answers<\/a> Chapter 9 Trigonometric Ratios and Functions<\/strong> and solve your issues within seconds. The perfect way to learn the concepts of ch 9 is by practicing the questions given in the BIM Math Book Algebra 2 Chapter 9 Trigonometric Ratios and Functions Solution Key. Look no further and start your preparation by using this quick &amp; ultimate guide. Constant practice can make you succeed in your math learning journey.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions<\/h2>\n<p>Enhance your math skills by taking the help of our provided Big Ideas Math Book Algebra 2 Ch 9 Trigonometric Ratios and Functions Solution key. After learning the concepts of the Algebra 2 9th chapters from the <strong>BIM Textbook Answers of Algebra 2,<\/strong> students can become math proficient. Access the Topicwise Big Ideas Math Book Algebra 2 Ch 9 Trigonometric Ratios and Functions Answers for free from the respective links presented below and prepare well for the exams.<\/p>\n<ul>\n<li><a href=\"#Trigonometric_Ratios_and_Functions_Maintaining_Mathematical_Proficiency\">Trigonometric Ratios and Functions Maintaining Mathematical Proficiency &#8211; Page 459<\/a><\/li>\n<li><a href=\"#Trigonometric_Ratios_and_Functions_Mathematical_Practices\">Trigonometric Ratios and Functions Mathematical Practices &#8211; Page 460<\/a><\/li>\n<li><a href=\"#Lesson_9.1_Right_Triangle_Trigonometry\">Lesson 9.1 Right Triangle Trigonometry &#8211; Page(461-468)<\/a><\/li>\n<li><a href=\"#Right_Triangle_Trigonometry_9.1_Exercises\">Right Triangle Trigonometry 9.1 Exercises &#8211; Page(466-468)<\/a><\/li>\n<li><a href=\"#Lesson_9.2_Angles_and_Radian_Measure\">Lesson 9.2 Angles and Radian Measure &#8211; Page(469-476)<\/a><\/li>\n<li><a href=\"#Angles_and_Radian_Measure_9.2_Exercises\">Angles and Radian Measure 9.2 Exercises &#8211; Page(474-476)<\/a><\/li>\n<li><a href=\"#Lesson_9.3_Trigonometric_Functions_of_Any_Angle\">Lesson 9.3 Trigonometric Functions of Any Angle &#8211; Page(477-484)<\/a><\/li>\n<li><a href=\"#Trigonometric_Functions_of_Any_Angle_9.3_Exercises\">Trigonometric Functions of Any Angle 9.3 Exercises &#8211; Page(482-484)<\/a><\/li>\n<li><a href=\"#Lesson_9.4_Graphing_Sine_and_Cosine_Functions\">Lesson 9.4 Graphing Sine and Cosine Functions &#8211; Page(485-494)<\/a><\/li>\n<li><a href=\"#Graphing_Sine_and_Cosine_Functions_9.4_Exercises\">Graphing Sine and Cosine Functions 9.4 Exercises &#8211; Page(491-494)<\/a><\/li>\n<li><a href=\"#Trigonometric_Ratios_and_Functions_Study_Skills:_Form_a_Final_Exam_Study_Group\">Trigonometric Ratios and Functions Study Skills: Form a Final Exam Study Group &#8211; Page 495<\/a><\/li>\n<li><a href=\"#Trigonometric_Ratios_and_Functions_9.1\u20139.4_Quiz\">Trigonometric Ratios and Functions 9.1\u20139.4 Quiz &#8211; Page 496<\/a><\/li>\n<li><a href=\"#Lesson_9.5_Graphing_Other_Trigonometric_Functions\">Lesson 9.5 Graphing Other Trigonometric Functions &#8211; Page(497-504)<\/a><\/li>\n<li><a href=\"#Graphing_Other_Trigonometric_Functions_9.5_Exercises\">Graphing Other Trigonometric Functions 9.5 Exercises &#8211; Page(502-504)<\/a><\/li>\n<li><a href=\"#Lesson_9.6_Modeling_with_Trigonometric_Functions\">Lesson 9.6 Modeling with Trigonometric Functions &#8211; Page(505-512)<\/a><\/li>\n<li><a href=\"#Modeling_with_Trigonometric_Functions_9.6_Exercises\">Modeling with Trigonometric Functions 9.6 Exercises &#8211; Page(510-512)<\/a><\/li>\n<li><a href=\"#Lesson_9.7_Using_Trigonometric_Identities\">Lesson 9.7 Using Trigonometric Identities &#8211; Page(513-518)<\/a><\/li>\n<li><a href=\"#Using_Trigonometric_Identities_9.7_Exercises\">Using Trigonometric Identities 9.7 Exercises &#8211; Page(517-518)<\/a><\/li>\n<li><a href=\"#Lesson_9.8_Using_Sum_and_Difference_Formulas\">Lesson 9.8 Using Sum and Difference Formulas &#8211; Page(519-524)<\/a><\/li>\n<li><a href=\"#Using_Sum_and_Difference_Formulas_9.8_Exercises\">Using Sum and Difference Formulas 9.8 Exercises &#8211; Page(523-524)<\/a><\/li>\n<li><a href=\"#Trigonometric_Ratios_and_Functions_Performance_Task:_Lightening_the_Load\">Trigonometric Ratios and Functions Performance Task: Lightening the Load &#8211; Page 525<\/a><\/li>\n<li><a href=\"#Trigonometric_Ratios_and_Functions_Chapter_Review\">Trigonometric Ratios and Functions Chapter Review &#8211; Page(526-530)<\/a><\/li>\n<li><a href=\"#Trigonometric_Ratios_and_Functions_Chapter_Test\">Trigonometric Ratios and Functions Chapter Test &#8211; Page 531<\/a><\/li>\n<li><a href=\"#Trigonometric_Ratios_and_Functions_Cumulative_Assessment\">Trigonometric Ratios and Functions Cumulative Assessment &#8211; Page(532 &#8211; 533)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Trigonometric_Ratios_and_Functions_Maintaining_Mathematical_Proficiency\"><\/a>Trigonometric Ratios and Functions Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Order the expressions by value from least to greatest.<\/strong><br \/>\nQuestion 1.<br \/>\nlog<sub>2 <\/sub>x<br \/>\n\u22234\u2223, 2 \u2212 9\u2223, \u22236 + 4\u2223, \u2212 \u22237\u2223<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\u22239 \u2212 3\u2223, \u22230\u2223, \u2223\u22124\u2223, \\(\\frac{|-5|}{|2|}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\u2223\u22128<sup>3<\/sup>\u2223,\u2223\u22122 \u2022 8 \u2223, \u22239 \u2212 1\u2223, \u22239\u2223 + \u2223\u22122\u2223 \u2212 \u22231 \u2223<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\u2223\u22124 + 20\u2223, \u2212\u22234<sup>2<\/sup>\u2223, \u22235\u2223\u2212\u22233 \u2022 2 \u2223, \u2223\u221215\u2223<br \/>\nAnswer:<\/p>\n<p><strong>Find the missing side length of the triangle.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 1\" width=\"94\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 2\" width=\"233\" height=\"90\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 3\" width=\"174\" height=\"104\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 4\" width=\"113\" height=\"99\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 5\" width=\"104\" height=\"138\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 6\" width=\"140\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nThe line segments connecting the points (x<sub>1<\/sub>, y<sub>1<\/sub>), (x<sub>2<\/sub>, y<sub>1<\/sub>), and (x<sub>2<\/sub>, y<sub>2<\/sub>) form a triangle. Is the triangle a right triangle? Justify your answer.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Trigonometric_Ratios_and_Functions_Mathematical_Practices\"><\/a>Trigonometric Ratios and Functions Mathematical Practices<\/h3>\n<p>Mathematically proficient students reason quantitatively by creating valid representations of problems.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Find the exact coordinates of the point (x, y) on the unit circle.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-7.1-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 7.1 1\" width=\"199\" height=\"188\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-7.1-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 7.1 2\" width=\"192\" height=\"185\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-7.1-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 7.1 3\" width=\"196\" height=\"202\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_9.1_Right_Triangle_Trigonometry\"><\/a>Lesson 9.1 Right Triangle Trigonometry<\/h3>\n<p><strong>Essential Question<\/strong> How can you find a trigonometric function of an acute angle \u03b8?<br \/>\nConsider one of the acute angles \u03b8 of a right triangle. Ratios of a right triangle\u2019s side lengths are used to define the six trigonometric functions, as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39555\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 1\" width=\"528\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-1.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-1-300x110.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Trigonometric Functions of Special Angles<br \/>\nWork with a partner. Find the exact values of the sine, cosine, and tangent functions for the angles 30\u00b0, 45\u00b0, and 60\u00b0 in the right triangles shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 2\" width=\"404\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-2.png 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-2-300x108.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Exploring Trigonometric Identities<br \/>\nWork with a partner.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39557\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 3\" width=\"232\" height=\"198\" \/><br \/>\nUse the definitions of the trigonometric functions to explain why each trigonometric identity is true.<br \/>\na. sin \u03b8 = cos(90\u00b0 \u2212 \u03b8)<br \/>\nb. cos \u03b8 = sin(90\u00b0 \u2212 \u03b8)<br \/>\nc. sin \u03b8 =\\(\\frac{1}{\\csc \\theta}\\)<br \/>\nd. tan \u03b8 = \\(\\frac{1}{\\cot \\theta}\\)<br \/>\nUse the definitions of the trigonometric functions to complete each trigonometric identity.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39558\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 4\" width=\"463\" height=\"40\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-4.png 463w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-4-300x26.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you find a trigonometric function of an acute angle \u03b8?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse a calculator to find the lengths x and y of the legs of the right triangle shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 5\" width=\"217\" height=\"104\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Evaluate the six trigonometric functions of the angle \u03b8.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 6\" width=\"94\" height=\"86\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 7\" width=\"101\" height=\"77\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39562\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-8.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 8\" width=\"101\" height=\"75\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nIn a right triangle, \u03b8 is an acute angle and cos \u03b8 = \\(\\frac{7}{10}\\). Evaluate the other five trigonometric functions of \u03b8.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nFind the value of x for the right triangle shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 9\" width=\"96\" height=\"85\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Solve \u25b3ABC using the diagram at the left and the given measurements.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-10.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 10\" width=\"149\" height=\"85\" \/><br \/>\nQuestion 6.<br \/>\nB = 45\u00b0, c = 5<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nA = 32\u00b0, b = 10<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nA = 71\u00b0, c = 20<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nB = 60\u00b0, a = 7<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nIn Example 5, find the distance between B and C.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 6, estimate the height of the parasailer above the boat when the angle of elevation is 38\u00b0.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Right_Triangle_Trigonometry_9.1_Exercises\"><\/a>Right Triangle Trigonometry 9.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nIn a right triangle, the two trigonometric functions of \u03b8 that are defined using the lengths of the hypotenuse and the side adjacent to \u03b8 are __________ and __________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 1\" width=\"554\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-1.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-1-300x47.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nCompare an angle of elevation to an angle of depression.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain what it means to solve a right triangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 3\" width=\"561\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-3.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-3-300x30.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 11\" width=\"563\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-11.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-11-300x76.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201310, evaluate the six trigonometric functions of the angle \u03b8.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-12.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 12\" width=\"145\" height=\"110\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 5\" width=\"525\" height=\"429\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-5.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-5-300x245.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39567\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 13\" width=\"112\" height=\"113\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39568\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-14.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 14\" width=\"108\" height=\"86\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 7\" width=\"597\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-7.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-7-300x219.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 15\" width=\"154\" height=\"72\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-16.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 16\" width=\"129\" height=\"85\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 9\" width=\"561\" height=\"617\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-9.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-9-273x300.png 273w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-17.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 17\" width=\"137\" height=\"84\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>REASONING<\/strong><br \/>\nLet \u03b8 be an acute angle of a right triangle. Use the two trigonometric functions tan \u03b8 = \\(\\frac{4}{9}\\) and sec \u03b8 = \\(\\frac{\\sqrt{97}}{9}\\) to sketch and label the right triangle. Then evaluate the other four trigonometric functions of \u03b8.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 11\" width=\"525\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-11.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-11-300x155.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nEvaluate the six trigonometric functions of the 90\u00b0 \u2212 \u03b8 angle in Exercises 5\u201310. Describe the relationships you notice.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201318, let \u03b8 be an acute angle of a right triangle. Evaluate the other five trigonometric functions of \u03b8.<\/strong><br \/>\nQuestion 13.<br \/>\nsin \u03b8 = \\(\\frac{7}{11}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-13.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 13.1\" width=\"575\" height=\"587\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-13.1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-13.1-294x300.png 294w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-13.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 13.2\" width=\"369\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-13.2.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-13.2-300x152.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/p>\n<p>Question 14.<br \/>\ncos \u03b8 = \\(\\frac{5}{12}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ntan \u03b8 = \\(\\frac{7}{6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-15.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 15.1\" width=\"571\" height=\"588\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-15.1.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-15.1-291x300.png 291w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-15.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 15.2\" width=\"409\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-15.2.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-15.2-300x156.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/p>\n<p>Question 16.<br \/>\ncsc \u03b8 = \\(\\frac{15}{8}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nsec \u03b8 = \\(\\frac{14}{9}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-17.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 17.1\" width=\"580\" height=\"592\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-17.1.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-17.1-294x300.png 294w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-17.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 17.2\" width=\"431\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-17.2.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-17.2-300x135.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p>Question 18.<br \/>\ncot \u03b8 = \\(\\frac{16}{11}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding sin \u03b8 of the triangle below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39572\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-18.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 18\" width=\"251\" height=\"167\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 19\" width=\"481\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-19.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-19-300x56.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding csc \u03b8, given that \u03b8 is an acute angle of a right triangle and cos \u03b8 = \\(\\frac{7}{11}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 19\" width=\"247\" height=\"66\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u201326, find the value of x for the right triangle.<\/strong><br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39574\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-20.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 20\" width=\"80\" height=\"99\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 21\" width=\"598\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-21.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-21-300x141.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 21\" width=\"84\" height=\"97\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39576\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-22.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 22\" width=\"83\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 23\" width=\"583\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-23.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-23-300x125.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39577\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-23.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 23\" width=\"100\" height=\"100\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39578\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-24.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 24\" width=\"104\" height=\"104\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 25\" width=\"575\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-25.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-25-300x127.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39579\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-25.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 25\" width=\"107\" height=\"102\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS <\/strong>In Exercises 27\u201332, evaluate the trigonometric function using a calculator. Round your answer to four decimal places.<br \/>\nQuestion 27.<br \/>\ncos 14\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 27\" width=\"192\" height=\"27\" \/><\/p>\n<p>Question 28.<br \/>\ntan 31\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\ncsc 59\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 29\" width=\"268\" height=\"52\" \/><\/p>\n<p>Question 30.<br \/>\nsin 23\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\ncot 6\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 31\" width=\"261\" height=\"52\" \/><\/p>\n<p>Question 32.<br \/>\nsec 11\u00b0<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 33\u201340, solve \u25b3ABC using the diagram and the given measurements.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-26.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 26.1\" width=\"105\" height=\"82\" \/><br \/>\nQuestion 33.<br \/>\nB = 36\u00b0, a = 23<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 33\" width=\"570\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-33.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-33-300x204.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 34.<br \/>\nA = 27\u00b0, b = 9<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nA = 55\u00b0, a = 17<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 35\" width=\"583\" height=\"392\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-35.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-35-300x202.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 36.<br \/>\nB = 16\u00b0, b = 14<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nA = 43\u00b0, b = 31<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 37\" width=\"598\" height=\"380\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-37.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-37-300x191.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 38.<br \/>\nB = 31\u00b0, a = 23<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nB = 72\u00b0, c = 12.8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 39\" width=\"596\" height=\"353\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-39.png 596w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-39-300x178.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/p>\n<p>Question 40.<br \/>\nA = 64\u00b0, a = 7.4<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nTo measure the width of a river, you plant a stake on one side of the river, directly across from a boulder. You then walk 100 meters to the right of the stake and measure a 79\u00b0 angle between the stake and the boulder. What is the width w of the river?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-26.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 26\" width=\"261\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 41\" width=\"295\" height=\"157\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nKatoomba Scenic Railway in Australia is the steepest railway in the world. The railway makes an angle of about 52\u00b0 with the ground. The railway extends horizontally about 458 feet. What is the height of the railway?<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the Jin Mao Building in Shanghai, China. The person estimates the angle of elevation to the top of the building is about 80\u00b0. What is the approximate height of the building?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 43\" width=\"561\" height=\"432\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-43.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-43-300x231.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe Duquesne Incline in Pittsburgh, Pennsylvania, has an angle of elevation of 30\u00b0. The track has a length of about 800 feet. Find the height of the incline.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are standing on the Grand View Terrace viewing platform at Mount Rushmore, 1000 feet from the base of the monument.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-27.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 27\" width=\"296\" height=\"137\" \/><br \/>\na. You look up at the top of Mount Rushmore at an angle of 24\u00b0. How high is the top of the monument from where you are standing? Assume your eye level is 5.5 feet above the platform.<br \/>\nb. The elevation of the Grand View Terrace is 5280 feet. Use your answer in part (a) to find the elevation of the top of Mount Rushmore.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 45\" width=\"592\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-45.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-45-300x125.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>WRITING<\/strong><br \/>\nWrite a real-life problem that can be solved using a right triangle. Then solve your problem.<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe Tropic of Cancer is the circle of latitude farthest north of the equator where the Sun can appear directly overhead. It lies 23.5\u00b0 north of the equator, as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-28.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 28\" width=\"175\" height=\"118\" \/><br \/>\na. Find the circumference of the Tropic of Cancer using 3960 miles as the approximate radius of Earth.<br \/>\nb. What is the distance between two points on the Tropic of Cancer that lie directly across from each other?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 47\" width=\"515\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-47.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-47-300x101.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the figure to answer each question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39584\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-29.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 29\" width=\"160\" height=\"97\" \/><br \/>\na. Which side is adjacent to \u03b8?<br \/>\nb. Which side is opposite of \u03b8?<br \/>\nc. Does cos \u03b8 = sin(90\u00b0 \u2212 \u03b8)? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA passenger in an airplane sees two towns directly to the left of the plane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39585\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-30.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 30\" width=\"350\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-30.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-30-300x93.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\na. What is the distance d from the airplane to the first town?<br \/>\nb. What is the horizontal distance x from the airplane to the first town?<br \/>\nc. What is the distance y between the two towns? Explain the process you used to find your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 49\" width=\"550\" height=\"590\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-49.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-49-280x300.png 280w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou measure the angle of elevation from the ground to the top of a building as 32\u00b0. When you move 50 meters closer to the building, the angle of elevation is 53\u00b0. What is the height of the building?<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims it is possible to draw a right triangle so the values of the cosine function of the acute angles are equal. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 51\" width=\"590\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-51.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-51-300x43.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nConsider a semicircle with a radius of 1 unit, as shown below. Write the values of the six trigonometric functions of the angle \u03b8. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39586\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-31.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 31\" width=\"160\" height=\"88\" \/><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA procedure for approximating \u03c0 based on the work of Archimedes is to inscribe a regular hexagon in a circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39587\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-32.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 32\" width=\"149\" height=\"121\" \/><br \/>\na. Use the diagram to solve for x. What is the perimeter of the hexagon?<br \/>\nb. Show that a regular n-sided polygon inscribed in a\ue031circle of radius 1 has a perimeter of 2n \u2022 sin (\\(\\frac{180}{n}\\))\u00b0.<br \/>\nc. Use the result from part (b) to find an expression in terms of n that approximates \u03c0. Then evaluate the expression when n= 50.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-53.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 53\" width=\"530\" height=\"454\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-53.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-53-300x257.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency.<\/strong><\/p>\n<p><strong>Perform the indicated conversion.<\/strong><br \/>\nQuestion 54.<br \/>\n5 years to seconds<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n12 pints to gallons<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-55.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 55\" width=\"258\" height=\"65\" \/><\/p>\n<p>Question 56.<br \/>\n5.6 meters to millimeters<br \/>\nAnswer:<\/p>\n<p><strong>Find the circumference and area of the circle with the given radius or diameter.<\/strong><br \/>\nQuestion 57.<br \/>\nr = 6 centimeters<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-57.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 57\" width=\"232\" height=\"68\" \/><\/p>\n<p>Question 58.<br \/>\nr = 11 inches<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\nd = 14 feet<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.1-a-59.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.1 a 59\" width=\"251\" height=\"92\" \/><\/p>\n<h3><a id=\"Lesson_9.2_Angles_and_Radian_Measure\"><\/a>Lesson 9.2 Angles and Radian Measure<\/h3>\n<p><strong>Essential Question<\/strong> How can you find the measure of an angle in radians?<br \/>\nLet the vertex of an angle be at the origin, with one side of the angle on the positive x-axis. The radian measure of the angle is a measure of the intercepted arc length on a circle of radius 1. To convert between degree and radian measure, use the fact that \\(\\frac{\\pi \\text { radians }}{180^{\\circ}}\\) = 1.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing Radian Measures of Angles<br \/>\nWork with a partner. Write the radian measure of each angle with the given degree measure. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 1\" width=\"486\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-1.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-1-300x121.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing Degree Measures of Angles<br \/>\nWork with a partner. Write the degree measure of each angle with the given radian measure. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39589\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 2\" width=\"271\" height=\"221\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you find the measure of an angle in radians?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe figure shows an angle whose measure is 30 radians. What is the measure of the angle in degrees? How many times greater is 30 radians than 30 degrees? Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39590\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 3\" width=\"382\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-3.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-3-300x184.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Draw an angle with the given measure in standard position.<\/strong><br \/>\nQuestion 1.<br \/>\n65\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n300\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\u2212120\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\u2212450\u00b0<br \/>\nAnswer:<\/p>\n<p><strong>Find one positive angle and one negative angle that are coterminal with the given angle.<\/strong><br \/>\nQuestion 5.<br \/>\n80\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n230\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n740\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\u2212135\u00b0<br \/>\nAnswer:<\/p>\n<p><strong>Convert the degree measure to radians or the radian measure to degrees.<\/strong><br \/>\nQuestion 9.<br \/>\n135\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n\u221240\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{5 \\pi}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n\u22126.28<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 4, the outfield fence is 220 feet from home plate. Estimate the length of the outfield fence and the area of the field.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Angles_and_Radian_Measure_9.2_Exercises\"><\/a>Angles and Radian Measure 9.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nAn angle is in standard position when its vertex is at the __________ and its __________ lies on the positive x-axis.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 1\" width=\"582\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-1.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-1-300x32.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how the sign of an angle measure determines its direction of rotation.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIn your own words, define a radian.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 3\" width=\"546\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-3.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-3-300x46.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich angle does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39591\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 4\" width=\"434\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-4.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-4-300x35.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u20138, draw an angle with the given measure in standard position.<\/strong><br \/>\nQuestion 5.<br \/>\n110\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 5\" width=\"544\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-5.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-5-300x194.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 6.<br \/>\n450\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\u2212900\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 7\" width=\"534\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-7.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-7-300x196.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 8.<br \/>\n\u221210\u00b0<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201312, find one positive angle and one negative angle that are coterminal with the given angle.<\/strong><br \/>\nQuestion 9.<br \/>\n70\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 9\" width=\"220\" height=\"69\" \/><\/p>\n<p>Question 10.<br \/>\n255\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\u2212125\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 11\" width=\"239\" height=\"66\" \/><\/p>\n<p>Question 12.<br \/>\n\u2212800\u00b0<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201320, convert the degree measure to radians or the radian measure to degrees.<\/strong><br \/>\nQuestion 13.<br \/>\n40\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 13\" width=\"307\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-13.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-13-300x104.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 14.<br \/>\n315\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\u2212260\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 15\" width=\"384\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-15.png 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-15-300x80.png 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/p>\n<p>Question 16.<br \/>\n\u2212500\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{\\pi}{9}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 17\" width=\"282\" height=\"88\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{3 \\pi}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\u22125<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 19\" width=\"327\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-19.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-19-300x83.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p>Question 20.<br \/>\n12<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>WRITING<\/strong><br \/>\nThe terminal side of an angle in standard position rotates one-sixth of a revolution counterclockwise from the positive x-axis. Describe how to find the measure of the angle in both degree and radian measures.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 21\" width=\"562\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-21.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-21-300x58.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nUsing radian measure, give one positive angle and one negative angle that are coterminal with the angle shown. Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 5\" width=\"189\" height=\"142\" \/><br \/>\nAnswer:<\/p>\n<p><strong>ANALYZING RELATIONSHIPS<\/strong> In Exercises 23\u201326, match the angle measure with the angle.<br \/>\nQuestion 23.<br \/>\n600\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 23\" width=\"586\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-23.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-23-300x43.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 24.<br \/>\n\\(-\\frac{9 \\pi}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n\\(\\frac{5 \\pi}{6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 25\" width=\"574\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-25.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-25-300x62.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 26.<br \/>\n\u2212240\u00b0<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39593\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 6\" width=\"365\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-6.png 365w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-6-300x214.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><\/p>\n<p>Question 27.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe observation deck of a building forms a sector with the dimensions shown. Find the length of the safety rail and the area of the deck.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 7\" width=\"201\" height=\"124\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 27\" width=\"578\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-27.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-27-300x128.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn the men\u2019s shot put event at the 2012 Summer Olympic Games, the length of the winning shot was 21.89 meters. A shot put must land within a sector having a central angle of 34.92\u00b0 to be considered fair.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39595\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-8.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 8\" width=\"247\" height=\"171\" \/><br \/>\na. The officials draw an arc across the fair landing area, marking the farthest throw. Find the length of the arc.<br \/>\nb. All fair throws in the 2012 Olympics landed within a sector bounded by the arc in part (a). What is the area of this sector?<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in converting the degree measure to radians.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 9\" width=\"321\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-9.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-9-300x135.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 29\" width=\"309\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-29.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-29-300x171.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the area of a sector with a radius of 6 centimeters and a central angle of 40\u00b0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-10.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 10\" width=\"320\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-10.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-10-300x78.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nWhen a CD player reads information from the outer edge of a CD, the CD spins about 200 revolutions per minute. At that speed, through what angle does a point on the CD spin in one\ue031minute? Give your answer in both degree and radian measures.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 31\" width=\"363\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-31.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-31-300x84.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou work every Saturday from 9:00 A.M. to 5:00 P.M. Draw a diagram that shows the rotation completed by the hour hand of a clock during this time. Find the measure of the angle generated by the hour hand in both degrees and radians. Compare this angle with the angle generated by the minute hand from 9:00 A.M. to 5:00 P.M.<br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 33\u201338, use a calculator to evaluate the trigonometric function.<br \/>\nQuestion 33.<br \/>\ncos \\(\\frac{4 \\pi}{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 33\" width=\"186\" height=\"55\" \/><\/p>\n<p>Question 34.<br \/>\nsin \\(\\frac{7 \\pi}{8}\\)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ncsc \\(\\frac{10 \\pi}{11}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 35\" width=\"275\" height=\"87\" \/><\/p>\n<p>Question 36.<br \/>\ncot (\u2212 \\(\\frac{6 \\pi}{5}\\))<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ncot(\u221214)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 37\" width=\"328\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-37.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-37-300x55.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 38.<br \/>\ncos 6<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe rear windshield wiper of a car rotates 120\u00b0, as shown. Find the area cleared by the wiper.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39598\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 11\" width=\"249\" height=\"155\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 39\" width=\"469\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-39.png 469w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-39-300x207.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA scientist performed an experiment to study the effects of gravitational force on humans. In order for humans to experience twice Earth\u2019s gravity, they were placed in a centrifuge 58 feet long and spun at a rate of about 15 revolutions per minute.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-12.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 12\" width=\"291\" height=\"129\" \/><br \/>\na. Through how many radians did the people rotate each second?<br \/>\nb. Find the length of the arc through which the people rotated each second.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn astronomy, the terminator is the day-night line on a planet that divides the planet into daytime and nighttime regions. The terminator moves across the surface of a planet as the planet rotates. It takes about 4 hours for Earth\u2019s terminator to move across the continental United States. Through what angle has Earth rotated during this time? Give your answer in both degree and radian measures.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 13\" width=\"177\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-13.png 177w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-13-150x150.png 150w\" sizes=\"(max-width: 177px) 100vw, 177px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 41\" width=\"576\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-41.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-41-300x47.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph to find the measure of \u03b8. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-14.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 14\" width=\"219\" height=\"157\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA dartboard is divided into 20 sectors. Each sector is worth a point value from 1 to 20 and has shaded regions that double or triple this value. A sector is shown below. Find the areas of the entire sector, the double region, and the triple region.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 15\" width=\"321\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-15.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-15-300x134.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 43\" width=\"580\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-43.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-43-300x146.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\n\u03c0 is an irrational number, which means that it cannot be written as the ratio of two whole numbers. \u03c0 can, however, be written exactly as a continued fraction, as follows.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-16.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 16\" width=\"307\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-16.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-16-300x150.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that when the arc length of a sector equals the radius, the area can be given by A = \\(\\frac{s^{2}}{2}\\). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 45\" width=\"578\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-45.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-45-300x62.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA spiral staircase has 15 steps. Each step is a sector with a radius of 42 inches and a central angle of \\(\\frac{\\pi}{8}\\).<br \/>\na. What is the length of the arc formed by the outer edge of a step?<br \/>\nb. Through what angle would you rotate by climbing the stairs?<br \/>\nc. How many square inches of carpeting would you need to cover the 15 steps?<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nThere are 60 minutes in 1 degree of arc, and 60 seconds in 1 minute of arc. The notation 50\u00b0 30\u2032 10\u2033 represents an angle with a measure of 50 degrees, 30 minutes, and 10 seconds.<br \/>\na. Write the angle measure 70.55\u00b0 using the notation above.<br \/>\nb. Write the angle measure 110\u00b0 45\u2032 30\u2033 to the nearest hundredth of a degree. Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 47\" width=\"337\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-47.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-47-300x143.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Find the distance between the two points.<\/strong><br \/>\nQuestion 48.<br \/>\n(1, 4), (3, 6)<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n(\u22127, \u221213), (10, 8)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 49\" width=\"361\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-49.png 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-49-300x168.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><\/p>\n<p>Question 50.<br \/>\n(\u22123, 9), (\u22123, 16)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n(2, 12), (8, \u22125)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 51\" width=\"308\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-51.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-51-300x183.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/p>\n<p>Question 52.<br \/>\n(\u221214, \u221222), (\u221220, \u221232)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n(4, 16), (\u22121, 34)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.2 a 53\" width=\"310\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-53.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.2-a-53-300x181.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<h3><a id=\"Lesson_9.3_Trigonometric_Functions_of_Any_Angle\"><\/a>Lesson 9.3 Trigonometric Functions of Any Angle<\/h3>\n<p><strong>Essential Question<\/strong> How can you use the unit circle to define the trigonometric functions of any angle?<br \/>\nLet \u03b8 be an angle in standard position with (x, y) a point on the terminal side of \u03b8 and r = \\(\\sqrt{x^{2}+y^{2}}\\) \u2260 0. The six trigonometric functions of \u03b8 are defined as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 1\" width=\"480\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-1.png 480w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-1-300x84.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing Trigonometric Functions<br \/>\nWork with a partner. Find the sine, cosine, and tangent of the angle \u03b8 in standard position whose terminal side intersects the unit circle at the point (x, y) shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 2\" width=\"647\" height=\"390\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-2.png 647w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-2-300x181.png 300w\" sizes=\"(max-width: 647px) 100vw, 647px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nHow can you use the unit circle to define the trigonometric functions of any angle?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nFor which angles are each function undefined? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39606\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-3.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 3.1\" width=\"222\" height=\"183\" \/><br \/>\na. tangent<br \/>\nb. cotangent<br \/>\nc. secant<br \/>\nd. cosecant<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Evaluate the six trigonometric functions of \u03b8.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39607\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 3\" width=\"142\" height=\"150\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-4.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 4\" width=\"144\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39609\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 5\" width=\"155\" height=\"150\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse the unit circle to evaluate the six trigonometric functions of \u03b8 = 180\u00ba.<br \/>\nAnswer:<\/p>\n<p><strong>Sketch the angle. Then find its reference angle.<\/strong><br \/>\nQuestion 5.<br \/>\n210\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\u2212260\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{-7 \\pi}{9}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{15 \\pi}{4}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Evaluate the function without using a calculator.<\/strong><br \/>\nQuestion 9.<br \/>\ncos(\u2212210\u00ba)<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nsec \\(\\frac{11 \\pi}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nUse the model given in Example 5 to estimate the horizontal distance traveled by a track and field long jumper who jumps at an angle of 20\u00b0 and with an initial speed of 27 feet per second.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Trigonometric_Functions_of_Any_Angle_9.3_Exercises\"><\/a>Trigonometric Functions of Any Angle 9.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nA(n) ___________ is an angle in standard position whose terminal side lies on an axis.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 1\" width=\"540\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-1.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-1-300x32.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nGiven an angle \u03b8 in standard position with its terminal side in Quadrant III, explain how you can use a reference angle to find cos \u03b8.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, evaluate the six trigonometric functions of \u03b8.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-6.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 6\" width=\"146\" height=\"124\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 3\" width=\"629\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-3.png 629w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-3-300x200.png 300w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 7\" width=\"137\" height=\"128\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-8.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 8\" width=\"147\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 5\" width=\"542\" height=\"418\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-5.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-5-300x231.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39613\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 9\" width=\"137\" height=\"128\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-10.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 10\" width=\"143\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 7\" width=\"552\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-7.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-7-300x228.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39615\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 11\" width=\"144\" height=\"132\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201314, use the unit circle to evaluate the six trigonometric functions of \u03b8.<\/strong><br \/>\nQuestion 9.<br \/>\n\u03b8 = 0\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 9\" width=\"559\" height=\"596\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-9.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-9-281x300.png 281w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 10.<br \/>\n\u03b8 = 540\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\u03b8 = \\(\\frac{\\pi}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 11\" width=\"575\" height=\"579\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-11.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-11-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-11-150x150.png 150w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 12.<br \/>\n\u03b8 = \\(\\frac{7 \\pi}{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n\u03b8 = \u2212270\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-13.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 13\" width=\"569\" height=\"613\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-13.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-13-278x300.png 278w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 14.<br \/>\n\u03b8 = \u22122\u03c0<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 15\u201322, sketch the angle. Then find its reference angle.<\/strong><br \/>\nQuestion 15.<br \/>\n\u2212100\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 15\" width=\"576\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-15.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-15-300x177.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 16.<br \/>\n150\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n320\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-17.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 17\" width=\"576\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-17.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-17-300x176.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 18.<br \/>\n\u2212370\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{15 \\pi}{4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-19.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 19\" width=\"558\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-19.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-19-300x199.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{8 \\pi}{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n\u2212\\(\\frac{5 \\pi}{6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-21.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 21\" width=\"570\" height=\"386\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-21.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-21-300x203.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 22.<br \/>\n\u2212\\(\\frac{13 \\pi}{6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nLet (\u22123, 2) be a point on the terminal side of an angle \u03b8 in standard position. Describe and correct the error in finding tan \u03b8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39616\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-12.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 12\" width=\"226\" height=\"75\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-23.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 23\" width=\"365\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-23.png 365w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-23-300x72.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding a reference angle \u03b8\u2032 for \u03b8 = 650\u00b0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39617\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-13.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 13\" width=\"319\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-13.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-13-300x94.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 25\u201332, evaluate the function without using a calculator.<\/strong><br \/>\nQuestion 25.<br \/>\nsec 135\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-25.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 25\" width=\"562\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-25.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-25-300x49.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 26.<br \/>\ntan 240\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nsin(\u2212150\u00b0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-27.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 27\" width=\"577\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-27.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-27-300x57.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 28.<br \/>\ncsc(\u2212420\u00b0)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\ntan (\u2212\\(\\frac{3 \\pi}{4}\\))<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-29.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 29\" width=\"592\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-29.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-29-300x79.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 30.<br \/>\ncot (\\(\\frac{-8 \\pi}{3}\\))<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\ncos \\(\\frac{7 \\pi}{4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-31.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 31\" width=\"513\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-31.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-31-300x85.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 32.<br \/>\nsec \\(\\frac{11 \\pi}{6}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 33\u201336, use the model for horizontal distance given in Example 5.<\/strong><br \/>\nQuestion 33.<br \/>\nYou kick a football at an angle of 60\u00b0 with an initial speed of 49 feet per second. Estimate the horizontal distance traveled by the football.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-33.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 33\" width=\"470\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-33.png 470w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-33-300x121.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Question 34.<br \/>\nThe \u201cfrogbot\u201d is a robot designed for exploring rough terrain on other planets. It can jump at a 45\u00b0 angle with an initial speed of 14 feet per second. Estimate the horizontal distance the frogbot can jump on Earth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39618\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-14.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 14\" width=\"204\" height=\"123\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nAt what speed must the in-line skater launch himself off the ramp in order to land on the other side of the ramp?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39619\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 15\" width=\"307\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-15.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-15-300x133.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-35.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 35\" width=\"521\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-35.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-35-300x132.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 36.<br \/>\nTo win a javelin throwing competition, your last throw must travel a horizontal distance of at least 100 feet. You release the javelin at a 40\u00b0 angle with an initial speed of 71 feet per second. Do you win the competition? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA rock climber is using a rock climbing treadmill that is 10 feet long. The climber begins by lying horizontally on the treadmill, which is then rotated about its midpoint by 110\u00b0 so that the rock climber is climbing toward the top. If the midpoint of the treadmill is 6 feet above the ground, how high above the ground is the top of the treadmill?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39620\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-16.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 16\" width=\"225\" height=\"203\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-37.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 37\" width=\"582\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-37.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-37-300x103.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>REASONING<\/strong><br \/>\nA Ferris wheel has a radius of 75 feet. You board a car at the bottom of the Ferris wheel, which is 10 feet above the ground, and rotate 255\u00b0counterclockwise before the ride temporarily stops. How high above the ground are you when the ride stops? If the radius of the Ferris wheel is doubled, is your height above the ground doubled? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nA sprinkler at ground level is used to water a garden. The water leaving the sprinkler has an initial speed of 25 feet per second.<br \/>\na. Use the model for horizontal distance given in Example 5 to complete the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39621\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-17.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 17\" width=\"276\" height=\"238\" \/><br \/>\nb. Which value of \u03b8 appears to maximize the horizontal distance traveled by the water? Use the model for horizontal distance and the unit circle to explain why your answer makes sense.<br \/>\nc. Compare the horizontal distance traveled by the water when \u03b8 = (45 \u2212 k)\u00b0 with the distance when \u03b8 = (45 + k)\u00b0, for 0 &lt; k &lt; 45.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-39.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 39\" width=\"562\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-39.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-39-300x268.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYour school\u2019s marching band is performing at halftime during a football game. In the last formation, the band members form a circle 100 feet wide in the center of the field. You start at a point on the circle 100 feet from the goal line, march 300\u00b0 around the circle, and then walk toward the goal line to exit the field. How far from the goal line are you at the point where you leave the circle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-18.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 18\" width=\"303\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-18.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-18-300x180.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nUse symmetry and the given information to label the coordinates of the other points corresponding to special angles on the unit circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-19.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 19\" width=\"233\" height=\"198\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-41.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 41\" width=\"552\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-41.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-41-300x177.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nUse the interactive unit circle tool at BigIdeasMath.com to describe all values of \u03b8 for each situation.<br \/>\na. sin \u03b8 &gt; 0, cos \u03b8 &lt; 0, and tan \u03b8 &gt; 0<br \/>\nb. sin \u03b8 &gt; 0, cos \u03b8 &lt; 0, and tan \u03b8 &lt; 0<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nWrite tan \u03b8 as the ratio of two other trigonometric functions. Use this ratio to explain why tan 90\u00b0 is undefined but cot 90\u00b0 = 0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-43.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 43\" width=\"577\" height=\"189\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-43.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-43-300x98.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nDetermine whether each of the six trigonometric functions of \u03b8 is positive, negative, or zero. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39624\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-20.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 20\" width=\"142\" height=\"130\" \/><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nA line with slope m passes through the origin. An angle \u03b8 in standard position has a terminal side that coincides with the line. Use a trigonometric function to relate the slope of the line to the angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-45.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 45\" width=\"577\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-45.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-45-300x58.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that the only solution to the trigonometric equation tan \u03b8 = \\(\\sqrt{3}\\) is \u03b8= 60\u00b0. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nWhen two atoms in a molecule are bonded to a common atom, chemists are interested in both the bond angle and the lengths of the bonds. An ozone molecule is made up of two oxygen atoms bonded to a third oxygen atom, as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-21.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 21\" width=\"225\" height=\"137\" \/><br \/>\na. In the diagram, coordinates are given in picometers (pm). (Note: 1 pm = 10<sup>\u221212<\/sup> m) Find the coordinates (x, y) of the center of the oxygen atom in Quadrant II.<br \/>\nb. Find the distance d (in picometers) between the centers of the two unbonded oxygen atoms.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-47.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 47\" width=\"568\" height=\"364\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-47.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-47-300x192.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe latitude of a point on Earth is the degree measure of the shortest arc from that point to the equator. For example, the latitude of point P in the diagram equals the degree measure of arc PE. At what latitude \u03b8 is the circumference of the circle of latitude at P half the distance around the equator?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-22.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 22\" width=\"260\" height=\"182\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Find all real zeros of the polynomial function.<\/strong><br \/>\nQuestion 49.<br \/>\nf (x) = x<sup>4<\/sup> + 2x<sup>3<\/sup> + x<sup>2<\/sup> + 8x \u2212 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-49.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 49\" width=\"578\" height=\"344\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-49.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-49-300x179.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 50.<br \/>\nf(x) = x<sup>5<\/sup> + 4x<sup>4<\/sup> \u2212 14x<sup>3<\/sup> \u2212 14x<sup>2<\/sup> \u2212 15x\u2212 18<br \/>\nAnswer:<\/p>\n<p>Graph the function.<br \/>\nQuestion 51.<br \/>\nf(x) = 2(x+ 3)<sup>2<\/sup> (x \u2212 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-51.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 51.1\" width=\"588\" height=\"418\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-51.1.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-51.1-300x213.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-51.2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 51.2\" width=\"455\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-51.2.png 455w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-51.2-300x231.png 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\n<p>Question 52.<br \/>\nf(x) = \\(\\frac{1}{2}\\) (x \u2212 4)(x + 5)(x + 9)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\nf(x) = x<sup>2<\/sup>(x + 1)<sup>3<\/sup> (x \u2212 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-53.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 53.1\" width=\"574\" height=\"411\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-53.1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-53.1-300x215.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-53.2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.3 a 53.2\" width=\"516\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-53.2.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.3-a-53.2-300x244.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<h3><a id=\"Lesson_9.4_Graphing_Sine_and_Cosine_Functions\"><\/a>Lesson 9.4 Graphing Sine and Cosine Functions<\/h3>\n<p><strong>Essential Question<\/strong> What are the characteristics of the graphs of the sine and cosine functions?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Graphing the Sine FunctionWork with a partner.<br \/>\na. Complete the table for y= sin x, where x is an angle measure in radians.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 1\" width=\"471\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-1.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-1-300x110.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><br \/>\nb. Plot the points (x, y) from part (a). Draw a smooth curve through the points to sketch the graph of y = sin x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 2\" width=\"471\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-2.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-2-300x104.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><br \/>\nc. Use the graph to identify the x-intercepts, the x-values where the local maximums and minimums occur, and the intervals for which the function is increasing or decreasing over \u22122\u03c0 \u2264 x \u2264 2\u03c0. Is the sine function even, odd, or neither?<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Graphing the Cosine Function<br \/>\nWork with a partner.<br \/>\na. Complete a table for y= cos x using the same values of x as those used in Exploration 1.<br \/>\nb. Plot the points (x, y) from part (a) and sketch the graph of y= cos x.<br \/>\nc. Use the graph to identify the x-intercepts, the x-values where the local maximums and minimums occur, and the intervals for which the function is increasing or decreasing over \u22122\u03c0 \u2264 x \u2264 2\u03c0. Is the cosine function even, odd, or neither?<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nWhat are the characteristics of the graphs of the sine and cosine functions?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nDescribe the end behavior of the graph of y = sin x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 3\" width=\"221\" height=\"151\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Identify the amplitude and period of the function. Then graph the function and describe the graph of g as a transformation of the graph of its parent function.<br \/>\nQuestion 1.<br \/>\ng(x) = \\(\\frac{1}{4}\\)sin x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ng(x) = cos 2x<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ng(x) = 2 sin \u03c0x<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ng(x) = \\(\\frac{1}{3}\\) cos \\(\\frac{1}{2}\\)x<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function.<\/strong><br \/>\nQuestion 5.<br \/>\ng(x) = cos x+ 4<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\ng(x) = \\(\\frac{1}{2}\\)sin (x \u2212 \\(\\left.\\frac{\\pi}{2}\\right\\))<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ng(x) = sin(x + \u03c0) \u2212 1<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function.<\/strong><br \/>\nQuestion 8.<br \/>\ng(x) = \u2212cos (x + \\(\\left.\\frac{\\pi}{2}\\right\\))<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ng(x) = \u22123 sin \\(\\frac{1}{2}\\)x + 2<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\ng(x) = \u22122 cos 4x \u2212 1<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Sine_and_Cosine_Functions_9.4_Exercises\"><\/a>Graphing Sine and Cosine Functions 9.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe shortest repeating portion of the graph of a periodic function is called a(n) _________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 1\" width=\"539\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-1.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-1-300x32.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the amplitudes and periods of the functions y = \\(\\frac{1}{2}\\)cos x and y = 3 cos 2x.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is a phase shift? Give an example of a sine function that has a phase shift.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 3\" width=\"584\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-3.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-3-300x39.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is the midline of the graph of the function y = 2 sin 3(x + 1) \u2212 2?<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 5\u20138, determine whether the graph represents a periodic function. If so, identify the period.<br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 4\" width=\"149\" height=\"125\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 5\" width=\"498\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-5.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-5-300x19.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 5\" width=\"155\" height=\"129\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 6\" width=\"143\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 7\" width=\"367\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-7.png 367w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-7-300x29.png 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 7\" width=\"157\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201312, identify the amplitude and period of the graph of the function.<\/strong><br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 8\" width=\"145\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 9\" width=\"393\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-9.png 393w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-9-300x24.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 9\" width=\"161\" height=\"127\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 10\" width=\"141\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-11.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 11\" width=\"363\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-11.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-11-300x27.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 11\" width=\"153\" height=\"138\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201320, identify the amplitude and period of the function. Then graph the function and describe the graph of g as a transformation of the graph of its parent function.<\/strong><br \/>\nQuestion 13.<br \/>\ng(x) = 3 sin x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-13.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 13\" width=\"588\" height=\"574\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-13.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-13-300x293.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 14.<br \/>\ng(x) = 2 sin x<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ng(x) = cos 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-15.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 15\" width=\"558\" height=\"603\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-15.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-15-278x300.png 278w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 16.<br \/>\ng(x) = cos 4x<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\ng(x) = sin 2\u03c0x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-17.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 17\" width=\"580\" height=\"525\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-17.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-17-300x272.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 18.<br \/>\ng(x) = 3 sin 2x<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\ng(x) = \\(\\frac{1}{3}\\)cos 4x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-19.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 19\" width=\"569\" height=\"649\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-19.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-19-263x300.png 263w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 20.<br \/>\ng(x) = \\(\\frac{1}{2}\\)cos 4\u03c0x<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>ANALYZING EQUATIONS<\/strong><br \/>\nWhich functions have an amplitude of 4 and a period of 2?<br \/>\nA. y = 4 cos 2x<br \/>\nB. y = \u22124 sin \u03c0x<br \/>\nC. y = 2 sin 4x<br \/>\nD. y = 4 cos \u03c0x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-21.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 21\" width=\"576\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-21.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-21-300x116.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>WRITING EQUATIONS<\/strong><br \/>\nWrite an equation of the form y = a sin bx, where a &gt; 0 and b &gt; 0, so that the graph has the given amplitude and period.<br \/>\na. amplitude: 1<br \/>\nperiod: 5<br \/>\nb. amplitude: 10<br \/>\nperiod: 4<br \/>\nc. amplitude: 2<br \/>\nperiod: 2\u03c0<br \/>\nd. amplitude: \\(\\frac{1}{2}\\)<br \/>\nperiod: 3\u03c0<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe motion of a pendulum can be modeled by the function d = 4 cos 8\u03c0t, where d is the horizontal displacement (in inches) of the pendulum relative to its position at rest and t is the time (in seconds). Find and interpret the period and amplitude in the context of this situation. Then graph the function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-23.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 23\" width=\"581\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-23.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-23-300x200.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA buoy bobs up and down as waves go past. The vertical displacement y (in feet) of the buoy with respect to sea level can be modeled by y = 1.75 cos \\(\\frac{\\pi}{3}\\)t, where t is the time (in seconds). Find and interpret the period and amplitude in the context of the problem. Then graph the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 12\" width=\"235\" height=\"148\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 25\u201334, graph the function.<\/strong><br \/>\nQuestion 25.<br \/>\ng(x) = sin x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-25.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 25\" width=\"565\" height=\"627\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-25.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-25-270x300.png 270w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 26.<br \/>\ng(x) = cos x \u2212 4<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\ng(x) = cos (x \u2212 \\(\\frac{\\pi}{2}\\))<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-27.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 27\" width=\"571\" height=\"675\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-27.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-27-254x300.png 254w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 28.<br \/>\ng(x) = sin (x + \\(\\frac{\\pi}{4}\\))<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\ng(x) = 2 cos x \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-29.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 29\" width=\"573\" height=\"691\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-29.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-29-249x300.png 249w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 30.<br \/>\ng(x) = 3 sin x + 1<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\ng(x) = sin 2(x + \u03c0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-31.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 31\" width=\"575\" height=\"680\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-31.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-31-254x300.png 254w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 32.<br \/>\ng(x) = cos 2(x \u2212 \u03c0)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ng(x) = sin \\(\\frac{1}{2}\\)(x + 2\u03c0) + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-33.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 33\" width=\"567\" height=\"561\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-33.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-33-300x297.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 34.<br \/>\ng(x) = cos \\(\\frac{1}{2}\\)(x \u2212 3\u03c0) \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the period of the function y = sin \\(\\frac{2}{3}\\)x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-13.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 13\" width=\"320\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-13.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-13-300x92.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-35.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 35\" width=\"404\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-35.png 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-35-300x108.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in determining the point where the maximum value of the function y = 2 sin (x \u2212 \\(\\frac{\\pi}{4}\\)) occurs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-14.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 14\" width=\"319\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-14.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-14-300x108.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 37\u201340, describe the transformation of the graph of f represented by the function g<br \/>\nQuestion 37.<br \/>\nf(x) = cos x, g(x) = 2 cos (x \u2212 \\(\\frac{\\pi}{2}\\)) + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-37.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 37\" width=\"562\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-37.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-37-300x39.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 38.<br \/>\nf(x) = sin x, g(x) = 3 sin (x + \\(\\frac{\\pi}{4}\\)) \u2212 2<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nf(x) = sin x, g(x) = sin 3(x + 3\u03c0) \u2212 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-39.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 39\" width=\"582\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-39.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-39-300x52.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 40.<br \/>\nf(x) = cos x, g(x) = cos 6(x \u2212 \u03c0) + 9<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 41\u201348, graph the function.<\/strong><br \/>\nQuestion 41.<br \/>\ng(x) = \u2212cos x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-41.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 41\" width=\"564\" height=\"574\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-41.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-41-295x300.png 295w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 42.<br \/>\ng(x) = \u2212sin x \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\ng(x) = \u2212sin \\(\\frac{1}{2}\\)x \u2212 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-43.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 43\" width=\"579\" height=\"551\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-43.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-43-300x285.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 44.<br \/>\ng(x) = \u2212cos 2x + 1<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\ng(x) = \u2212sin(x \u2212 \u03c0) + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-45.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 45\" width=\"560\" height=\"620\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-45.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-45-271x300.png 271w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 46.<br \/>\ng(x) = \u2212cos(x + \u03c0) \u2212 2<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\ng(x) = \u22124 cos (x + \\(\\frac{\\pi}{4}\\)) \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-47.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 47\" width=\"579\" height=\"711\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-47.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-47-244x300.png 244w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 48.<br \/>\ng(x) = \u22125 sin (x \u2212 \\(\\frac{\\pi}{2}\\)) + 3<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nWhich of the following is a point where the maximum value of the graph of y =\u22124 cos (x \u2212 \\(\\frac{\\pi}{2}\\))occurs?<br \/>\nA. (\u2212\\(\\frac{\\pi}{2}\\), 4 )<br \/>\nB. (\\(\\frac{\\pi}{2}\\), 4 )<br \/>\nC. (0, 4)<br \/>\nD. (\u03c0, 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-49.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 49\" width=\"544\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-49.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-49-300x98.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nMatch each function with its graph. Explain your reasoning.<br \/>\na. y = 3 + sin x<br \/>\nb. y = \u22123 + cos x<br \/>\nc. y = sin 2(x \u2212 \\(\\frac{\\pi}{2}\\))<br \/>\nd. y = cos 2 (x \u2212 \\(\\frac{\\pi}{2}\\))<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-15.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 15\" width=\"360\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-15.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-15-300x220.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>WRITING EQUATIONS<\/strong> In Exercises 51\u201354, write a rule for g that represents the indicated transformations of the graph of f.<br \/>\nQuestion 51.<br \/>\nf(x) = 3 sin x; translation 2 units up and \u03c0 units right<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-51.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 51\" width=\"452\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-51.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-51-300x22.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 52.<br \/>\nf(x) = cos 2\u03c0x; translation 4 units down and 3 units left<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\nf(x) = \\(\\frac{1}{3}\\)cos \u03c0x; translation 1 unit down, followed by a reflection in the line y =\u22121<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-53.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 53\" width=\"425\" height=\"43\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-53.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-53-300x30.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Question 54.<br \/>\nf(x) = \\(\\frac{1}{2}\\) sin 6x; translation \\(\\frac{3}{2}\\) units down and 1 unit right, followed by a reflection in the line y = \u2212\\(\\frac{3}{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe height h(in feet) of a swing above the ground can be modeled by the function h = \u22128 cos \u03b8+ 10, where the pivot is 10 feet above the ground, the rope is 8 feet long, and \u03b8 is the angle that the rope makes with the vertical. Graph the function. What is the height of the swing when \u03b8 is 45\u00b0?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-16.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 16\" width=\"319\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-16.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-16-300x139.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-55.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 55\" width=\"453\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-55.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-55-300x196.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>DRAWING A CONCLUSION<\/strong><br \/>\nIn a particular region, the population L (in thousands) of lynx (the predator) and the population H (in thousands) of hares (the prey) can be modeled by the equations<br \/>\nL = 11.5 + 6.5 sin\\(\\frac{\\pi}{5}\\)t<br \/>\nH = 27.5 + 17.5 cos \\(\\frac{\\pi}{5}\\)t<br \/>\nwhere t is the time in years.<br \/>\na. Determine the ratio of hares to lynx when t = 0, 2.5, 5, and 7.5 years.<br \/>\nb. Use the figure to explain how the changes in the two populations appear to be related.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39643\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-17.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 17\" width=\"225\" height=\"180\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nThe average wind speed s (in miles per hour) in the Boston Harbor can be approximated by s = 3.38 sin\\(\\frac{\\pi}{180}\\)(t + 3) + 11.6 where t is the time in days and t = 0 represents January 1. Use a graphing calculator to graph the function. On which days of the year is the average wind speed 10 miles per hour? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-57.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 57\" width=\"593\" height=\"420\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-57.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-57-300x212.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nThe water depth d (in feet) for the Bay of Fundy can be modeled by d = 35 \u2212 28 cos \\(\\frac{\\pi}{6.2}\\)t, where t is the time in hours and t = 0 represents midnight. Use a graphing calculator to graph the function. At what time(s) is the water depth 7 feet? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-18.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 18\" width=\"297\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nFind the average rate of change of each function over the interval 0 &lt; x &lt; \u03c0.<br \/>\na. y = 2 cos x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-19.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 19\" width=\"341\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-19.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-19-300x190.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-59.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 59\" width=\"436\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-59.png 436w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-59-300x265.png 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>REASONING<\/strong><br \/>\nConsider the functions y = sin(\u2212x) and y = cos(\u2212x).<br \/>\na. Construct a table of values for each equation using the quadrantal angles in the interval \u22122\u03c0 \u2264 x \u2264 2\u03c0.<br \/>\nb. Graph each function.<br \/>\nc. Describe the transformations of the graphs of the parent functions.<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are riding a Ferris wheel that turns for 180 seconds. Your height h (in feet) above the ground at any time t (in seconds) can be modeled by the equation h = 85 sin\\(\\frac{\\pi}{20}\\)(t \u2212 10) + 90.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-20.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 20\" width=\"142\" height=\"148\" \/><br \/>\na. Graph the function.<br \/>\nb. How many cycles does the Ferris wheel make in 180 seconds?<br \/>\nc. What are your maximum and minimum heights?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-61.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 61\" width=\"587\" height=\"388\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-61.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-61-300x198.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph to answer each question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39647\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-21.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 21\" width=\"198\" height=\"155\" \/><br \/>\na. Does the graph represent a function of the form f(x) = a sin bx or f(x) =a cos bx? Explain.<br \/>\nb. Identify the maximum value, minimum value, period, and amplitude of the function.<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<strong>FINDING A PATTERN<\/strong><br \/>\nWrite an expression in terms of the integer n that represents all the x-intercepts of the graph of the function y = cos 2x. Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-63.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 63\" width=\"536\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-63.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-63-300x69.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend states that for functions of the form y = a sin bx and y = a cos bx, the values of a and b affect the x-intercepts of the graph of the function. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDescribe a transformation of the graph of f(x) = sin x that results in the graph of g(x) = cos x.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-65.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 65\" width=\"563\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-65.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-65-300x36.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 66.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nUse a graphing calculator to find a function of the form y = sin b<sub>1<\/sub>x + cos b<sub>2<\/sub>xwhose graph matches that shown below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-22.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 22\" width=\"327\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-22.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-22-300x120.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nFor a person at rest, the blood pressure P (in millimeters of mercury) at time t (in seconds) is given by the function<br \/>\nP = 100 \u2212 20 cos \\(\\frac{8 \\pi}{3}\\)t.<br \/>\nGraph the function. One cycle is equivalent to one heartbeat. What is the pulse rate (in heartbeats per minute) of the person?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-23.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 23\" width=\"196\" height=\"139\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45193\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-67.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 67\" width=\"559\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-67.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-67-300x94.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 68.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe motion of a spring can be modeled by y = A cos kt, where y is the vertical displacement (in feet) of the spring relative to its position at rest, A is the initial displacement (in feet), k is a constant that measures the elasticity of the spring, and t is the time (in seconds).<br \/>\na. You have a spring whose motion can be modeled by the function y= 0.2 cos 6t. Find the initial displacement and the period of the spring. Then graph the function.<br \/>\nb. When a damping force is applied to the spring, the motion of the spring can be modeled by the function y = 0.2e<sup>\u22124.5t<\/sup> cos 4t. Graph this function. What effect does damping have on the motion?<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Simplify the rational expression, if possible.<\/strong><br \/>\nQuestion 69.<br \/>\n\\(\\frac{x^{2}+x-6}{x+3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-69.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 69\" width=\"284\" height=\"94\" \/><\/p>\n<p>Question 70.<br \/>\n\\(\\frac{x^{3}-2 x^{2}-24 x}{x^{2}-2 x-24}\\)<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n\\(\\frac{x^{2}-4 x-5}{x^{2}+4 x-5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-71.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 71\" width=\"284\" height=\"61\" \/><\/p>\n<p>Question 72.<br \/>\n\\(\\frac{x^{2}-16}{x^{2}+x-20}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Find the least common multiple of the expressions.<\/strong><br \/>\nQuestion 73.<br \/>\n2x, 2(x \u2212 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-73.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 73\" width=\"558\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-73.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-73-300x17.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 74.<br \/>\nx<sup>2<\/sup> \u2212 4, x + 2<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\nx<sup>2<\/sup> + 8x + 12, x + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-75.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 a 75\" width=\"572\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-75.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-a-75-300x31.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<h3><a id=\"Trigonometric_Ratios_and_Functions_Study_Skills:_Form_a_Final_Exam_Study_Group\"><\/a>Trigonometric Ratios and Functions Study Skills: Form a Final Exam Study Group<\/h3>\n<p><strong>9.1\u20139.4 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-24.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 24\" width=\"613\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-24.png 613w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-24-300x77.png 300w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-25.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 25\" width=\"675\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-25.png 675w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-25-300x134.png 300w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nMake a conjecture about the horizontal distances traveled in part (c) of Exercise 39 on page 483.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nExplain why the quantities in part (a) of Exercise 56 on page 493 make sense in the context of the situation.<br \/>\nAnswer:<\/p>\n<p><strong>Study Skills: Form a Final Exam Study Group<\/strong><\/p>\n<p>Form a study group several weeks before the final exam. The intent of this group is to review what you have already learned while continuing to learn new material.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-26.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.4 26\" width=\"364\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-26.png 364w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.4-26-300x226.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<h3><a id=\"Trigonometric_Ratios_and_Functions_9.1\u20139.4_Quiz\"><\/a>Trigonometric Ratios and Functions 9.1\u20139.4 Quiz<\/h3>\n<p>Question 1.<br \/>\nIn a right triangle, \u03b8 is an acute angle and sin \u03b8 = \\(\\frac{1}{2}\\). Evaluate the other five trigonometric functions of \u03b8.<br \/>\nAnswer:<\/p>\n<p><strong>Find the value of x for the right triangle.<\/strong><br \/>\nQuestion 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions q 1\" width=\"193\" height=\"112\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-2.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions q 2\" width=\"173\" height=\"114\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions q 3\" width=\"99\" height=\"113\" \/><br \/>\nAnswer:<\/p>\n<p>Draw an angle with the given measure in standard position. Then find one positive angle and one negative angle that are coterminal with the given angle.<br \/>\nQuestion 5.<br \/>\n40\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{5 \\pi}{6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\u2212960\u00b0<br \/>\nAnswer:<\/p>\n<p><strong>Convert the degree measure to radians or the radian measure to degrees.<\/strong><br \/>\nQuestion 8.<br \/>\n\\(\\frac{3 \\pi}{10}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\u221260\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n72\u00b0<br \/>\nAnswer:<\/p>\n<p><strong>Evaluate the six trigonometric functions of \u03b8.<\/strong><br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-4.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions q 4\" width=\"170\" height=\"143\" \/><br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions q 5\" width=\"152\" height=\"144\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-6.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions q 6\" width=\"158\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-6.png 158w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-6-150x150.png 150w\" sizes=\"(max-width: 158px) 100vw, 158px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nIdentify the amplitude and period of g(x) = 3 sin x. Then graph the function and describe the graph of g as a transformation of the graph of f (x) = sin x.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nIdentify the amplitude and period of g(x) = cos 5\u03c0x + 3. Then graph the function and describe the graph of g as a transformation of the graph of f(x) = cos x.<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nYou are flying a kite at an angle of 70\u00b0. You have let out a total of 400 feet of string and are holding the reel steady 4 feet above the ground.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 9 Trigonometric Ratios and Functions q 7\" width=\"303\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-7.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-q-7-300x188.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\na. How high above the ground is the kite?<br \/>\nb. A friend watching the kite estimates that the angle of elevation to the kite is 85\u00b0. How far from your friend are you standing?<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nThe top of the Space Needle in Seattle, Washington, is a revolving, circular restaurant. The restaurant has a radius of 47.25 feet and makes one complete revolution in about an hour. You have dinner at a window table from 7:00 P.M. to 8:55 P.M. Compare the distance you revolve with the distance of a person seated 5 feet away from the windows.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_9.5_Graphing_Other_Trigonometric_Functions\"><\/a>Lesson 9.5 Graphing Other Trigonometric Functions<\/h3>\n<p><strong>Essential Question<\/strong> What are the characteristics of the graph of the tangent function?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Graphing the Tangent Function<br \/>\nWork with a partner. a. Complete the table for y = tan x, where x is an angle measure in radians.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 1\" width=\"468\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-1.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-1-300x103.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\nb. The graph of y = tan x has vertical asymptotes at x-values where tan x is undefined. Plot the points (x, y) from part (a). Then use the asymptotes to sketch the graph of y = tan x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-2.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 2\" width=\"343\" height=\"353\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-2.png 343w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-2-292x300.png 292w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><br \/>\nc. For the graph of y = tan x, identify the asymptotes, the x-intercepts, and the intervals for which the function is increasing or decreasing over \u2212\\(\\frac{\\pi}{2}\\) \u2264 x \u2264 \\(\\frac{3 \\pi}{2}\\). Is the tangent function even, odd, or neither?<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nWhat are the characteristics of the graph of the tangent function?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nDescribe the asymptotes of the graph of y = cot x on the interval \u2212\\(\\frac{\\pi}{2}\\) &lt; x &lt; \\(\\frac{3 \\pi}{2}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 3\" width=\"219\" height=\"207\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Graph one period of the function. Describe the graph of g as a transformation of the graph of its parent function.<\/strong><br \/>\nQuestion 1.<br \/>\ng(x) = tan 2x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ng(x) = \\(\\frac{1}{3}\\)cot x<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ng(x) = 2 cot 4x<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ng(x) = 5 tan \u03c0x<br \/>\nAnswer:<\/p>\n<p><strong>Graph one period of the function. Describe the graph of g as a transformation of the graph of its parent function.<\/strong><br \/>\nQuestion 5.<br \/>\ng(x) = csc 3x<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\ng(x) = \\(\\frac{1}{2}\\)sec x<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ng(x) = 2 csc 2x<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ng(x) = 2 sec \u03c0x<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Other_Trigonometric_Functions_9.5_Exercises\"><\/a>Graphing Other Trigonometric Functions 9.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why the graphs of the tangent, cotangent, secant, and cosecant functions do not have an amplitude.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 1\" width=\"575\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-1-300x41.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe _______ and _______ functions are undefined for x-values at which sin x = 0.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe period of the function y = sec x is _____, and the period of y = cot x is _____.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45199\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 3\" width=\"571\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-3.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-3-300x31.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to graph a function of the form y = a sec bx.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201312, graph one period of the function. Describe the graph of gas a transformation of the graph of its parent function.<\/strong><br \/>\nQuestion 5.<br \/>\ng(x) = 2 tan x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 5\" width=\"603\" height=\"673\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-5.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-5-269x300.png 269w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Question 6.<br \/>\ng(x) = 3 tan x<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ng(x) = cot 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 7\" width=\"591\" height=\"639\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-7.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-7-277x300.png 277w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 8.<br \/>\ng(x) = cot 2x<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ng(x) = 3 cot \\(\\frac{1}{4}\\)x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-9.1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 9.1\" width=\"554\" height=\"469\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-9.1.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-9.1-300x254.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-9.2.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 9.2\" width=\"547\" height=\"390\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-9.2.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-9.2-300x214.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 10.<br \/>\ng(x) = 4 cot\\(\\frac{1}{2}\\)x<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ng(x) = \\(\\frac{1}{2}\\)tan \u03c0x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-11.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 11\" width=\"605\" height=\"695\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-11.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-11-261x300.png 261w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p>Question 12.<br \/>\ng(x) = \\(\\frac{1}{3}\\) tan 2\u03c0x<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the period of the function y = cot 3x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-4.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 4\" width=\"229\" height=\"75\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-13.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 13\" width=\"411\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-13.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-13-300x75.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in describing the transformation of f(x) = tan x represented by g(x) = 2 tan 5x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 5\" width=\"319\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-5.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-5-300x65.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nUse the given graph to graph each function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39665\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-6.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 6\" width=\"321\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-6.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-6-300x151.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-15.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 15\" width=\"313\" height=\"585\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-15.png 313w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-15-161x300.png 161w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/p>\n<p>Question 16.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nWhich of the following are asymptotes of the graph of y = 3 tan 4x?<br \/>\nA. x = \\(\\frac{\\pi}{8}\\)<br \/>\nB. x = \\(\\frac{\\pi}{4}\\)<br \/>\nC. x = 0<br \/>\nD. x = \u2212\\(\\frac{5 \\pi}{8}\\)<br \/>\nAnswer:<\/p>\n<p>In Exercises 17\u201324, graph one period of the function. Describe the graph of gas a transformation of the graph of its parent function.<br \/>\nQuestion 17.<br \/>\ng(x) = 3 csc x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-17.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 17\" width=\"584\" height=\"637\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-17.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-17-275x300.png 275w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 18.<br \/>\ng(x) = 2 csc x<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\ng(x) = sec 4x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-19.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 19\" width=\"568\" height=\"555\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-19.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-19-300x293.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 20.<br \/>\ng(x) = sec 3x<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\ng(x) = \\(\\frac{1}{2}\\)sec \u03c0x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-21.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 21\" width=\"580\" height=\"619\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-21.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-21-281x300.png 281w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 22.<br \/>\ng(x) = \\(\\frac{1}{4}\\) sec 2\u03c0x<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\ng(x) = csc \\(\\frac{\\pi}{2}\\)x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-23.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 23\" width=\"563\" height=\"545\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-23.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-23-300x290.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 24.<br \/>\ng(x) = csc \\(\\frac{\\pi}{4}\\)x<br \/>\nAnswer:<\/p>\n<p><strong>ATTENDING TO PRECISION<\/strong> In Exercises 25\u201328, use the graph to write a function of the form y = a tan bx.<br \/>\nQuestion 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 7\" width=\"123\" height=\"134\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-25.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 25\" width=\"554\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-25.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-25-300x38.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-8.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 8\" width=\"134\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-9.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 9\" width=\"130\" height=\"134\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-27.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 27\" width=\"563\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-27.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-27-300x43.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-10.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 10\" width=\"147\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 29\u201334, match the equation with the correct graph. Explain your reasoning.<br \/>\nQuestion 29.<br \/>\ng(x) = 4 tan x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-29.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 29\" width=\"562\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-29.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-29-300x42.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 30.<br \/>\ng(x) = 4 cot x<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\ng(x) = 4 csc \u03c0x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-31.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 31\" width=\"575\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-31.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-31-300x31.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 32.<br \/>\ng(x) = 4 sec \u03c0x<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ng(x) = sec 2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-33.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 33\" width=\"575\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-33.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-33-300x43.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 34.<br \/>\ng(x) = csc 2x<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-11.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 11\" width=\"336\" height=\"412\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-11.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-11-245x300.png 245w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>Question 35.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why there is more than one tangent function whose graph passes through the origin and has asymptotes at x = \u2212\u03c0 and x = \u03c0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-35.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 35\" width=\"557\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-35.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-35-300x59.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nGraph one period of each function. Describe the transformation of the graph of its parent function.<br \/>\na. g(x) = sec x + 3<br \/>\nb. g(x) = csc x \u2212 2<br \/>\nc. g(x) = cot(x \u2212 \u03c0)<br \/>\nd. g(x) = \u2212tan x<br \/>\nAnswer:<\/p>\n<p><strong>WRITING EQUATIONS<\/strong> In Exercises 37\u201340, write a rule for g that represents the indicated transformation of the graph of f.<br \/>\nQuestion 37.<br \/>\nf(x) = cot 2x; translation 3 units up and \\(\\frac{\\pi}{2}\\) units left<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-37.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 37\" width=\"556\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-37.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-37-300x28.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 38.<br \/>\nf(x) = 2 tan x; translation \u03c0 units right, followed by a horizontal shrink by a factor of \\(\\frac{1}{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nf(x) = 5 sec (x \u2212 \u03c0); translation 2 units down, followed by a reflection in the x-axis<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-39.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 39\" width=\"569\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-39.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-39-300x16.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 40.<br \/>\nf(x) = 4 csc x; vertical stretch by a factor of 2 and a reflection in the x-axis<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nWhich function has a greater local maximum value? Which has a greater local minimum value? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-12.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 12\" width=\"356\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-12.png 356w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-12-300x120.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45219\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-41.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 41\" width=\"576\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-41.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-41-300x67.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nOrder the functions from the least average rate of change to the greatest average rate of change over the interval \u2212\\(\\frac{\\pi}{4}\\) &lt; x &lt; \\(\\frac{\\pi}{4}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-13.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 13\" width=\"341\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-13.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-13-300x235.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou are standing on a bridge 140 feet above the ground. You look down at a car traveling away from the underpass. The distance d (in feet) the car is from the base of the bridge can be modeled by d= 140 tan \u03b8. Graph the function. Describe what happens to \u03b8 as d increases<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-14.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 14\" width=\"286\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-43.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 43\" width=\"536\" height=\"321\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-43.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-43-300x180.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nYou use a video camera to pan up the Statue of Liberty. The height h (in feet) of the part of the Statue of Liberty that can be seen through your video camera after time t (in seconds) can be modeled by h= 100 tan \\(\\frac{\\pi}{36}\\)t. Graph the function using a graphing calculator. What viewing window did you use? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are standing 120 feet from the base of a 260-foot building. You watch your friend go down the side of the building in a glass elevator.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-15.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 15\" width=\"262\" height=\"156\" \/><br \/>\na. Write an equation that gives the distance d (in feet) your friend is from the top of the building as a function of the angle of elevation \u03b8.<br \/>\nb. Graph the function found in part (a). Explain how the graph relates to this situation.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45221\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-45.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 45\" width=\"579\" height=\"480\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-45.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-45-300x249.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are standing 300 feet from the base of a 200-foot cliff. Your friend is rappelling down the cliff.<br \/>\na. Write an equation that gives the distance d(in feet) your friend is from the top of the cliff as a function of the angle of elevation \u03b8.<br \/>\nb. Graph the function found in part (a).<br \/>\nc. Use a graphing calculator to determine the angle of elevation when your friend has rappelled halfway down the cliff.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-16.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 16\" width=\"126\" height=\"143\" \/><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend states that it is not possible to write a cosecant function that has the same graph as y = sec x. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-47.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 47\" width=\"575\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-47.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-47-300x40.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph to answer each question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-17.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 17\" width=\"164\" height=\"143\" \/><br \/>\na. What is the period of the graph?<br \/>\nb. What is the range of the function?<br \/>\nc. Is the function of the form f(x) = a csc bx or f(x) = a sec bx? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nRewrite a sec bx in terms of cos bx. Use your results to explain the relationship between the local maximums and minimums of the cosine and secant functions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-49.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 49\" width=\"549\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-49.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-49-300x108.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nA trigonometric equation that is true for all values of the variable for which both sides of the equation are defined is called a trigonometric identity.Use a graphing calculator to graph the function<br \/>\ny = \\(\\frac{1}{2}\\)(tan \\(\\frac{x}{2}\\) + cot \\(\\frac{x}{2}\\)) .<br \/>\nUse your graph to write a trigonometric identity involving this function. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nFind a tangent function whose graph intersects the graph of y = 2 + 2 sin x only at minimum points of the sine function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-51.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 51\" width=\"357\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-51.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-51-300x50.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write a cubic function whose graph passes through the given points.<\/strong><br \/>\nQuestion 52.<br \/>\n(\u22121, 0), (1, 0), (3, 0), (0, 3)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n(\u22122, 0), (1, 0), (3, 0), (0, \u22126)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-53.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 53\" width=\"574\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-53.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-53-300x167.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 54.<br \/>\n(\u22121, 0), (2, 0), (3, 0), (1, \u22122)<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n(\u22123, 0), (\u22121, 0), (3, 0), (\u22122, 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45226\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-55.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 55\" width=\"572\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-55.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-55-300x201.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p><strong>Find the amplitude and period of the graph of the function.<\/strong><br \/>\nQuestion 56.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-18.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 18\" width=\"154\" height=\"148\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-19.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 19\" width=\"164\" height=\"139\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-57.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 a 57\" width=\"373\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-57.png 373w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-a-57-300x24.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>Question 58.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-9.5-20.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions 9.5 20\" width=\"153\" height=\"139\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_9.6_Modeling_with_Trigonometric_Functions\"><\/a>Lesson 9.6 Modeling with Trigonometric Functions<\/h3>\n<p><strong>Essential Question<\/strong> What are the characteristics of the real-life problems that can be modeled by trigonometric functions?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Modeling Electric Currents<br \/>\nWork with a partner. Find a sine function that models the electric current shown in each oscilloscope screen. State the amplitude and period of the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 1\" width=\"714\" height=\"609\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-1.png 714w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-1-300x256.png 300w\" sizes=\"(max-width: 714px) 100vw, 714px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nWhat are the characteristics of the real-life problems that can be modeled by trigonometric functions?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nUse the Internet or some other reference to find examples of real-life situations that can be modeled by trigonometric functions.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nWHAT IF?<br \/>\nIn Example 1, how would the function change when the audiometer produced a pure tone with a frequency of 1000 hertz?<br \/>\nAnswer:<\/p>\n<p><strong>Write a function for the sinusoid.<\/strong><br \/>\nQuestion 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39683\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 2\" width=\"205\" height=\"140\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 3\" width=\"204\" height=\"148\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nDescribe how the model in Example 3 changes when the lowest point of a rope is 5 inches above the ground and the highest point is 70 inches above the ground.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nThe table shows the average daily temperature T (in degrees Fahrenheit) for a city each month, where m = 1 represents January. Write a model that gives T as a function of m and interpret the period of its graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 4\" width=\"475\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-4.png 475w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-4-300x42.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Modeling_with_Trigonometric_Functions_9.6_Exercises\"><\/a>Modeling with Trigonometric Functions 9.6 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nGraphs of sine and cosine functions are called __________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 1\" width=\"522\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-1.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-1-300x20.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe how to find the frequency of the function whose graph is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 5\" width=\"154\" height=\"118\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, find the frequency of the function.<\/strong><br \/>\nQuestion 3.<br \/>\ny = sin x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 3\" width=\"210\" height=\"140\" \/><\/p>\n<p>Question 4.<br \/>\ny = sin 3x<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\ny = cos 4x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 5\" width=\"210\" height=\"250\" \/><\/p>\n<p>Question 6.<br \/>\ny =\u2212cos 2x<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ny = sin 3\u03c0x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 7\" width=\"218\" height=\"259\" \/><\/p>\n<p>Question 8.<br \/>\ny = cos \\(\\frac{\\pi x}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = \\(\\frac{1}{2}\\) cos 0.75x \u2212 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 9\" width=\"209\" height=\"259\" \/><\/p>\n<p>Question 10.<br \/>\ny = 3 sin 0.2x + 6<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe lowest frequency of sounds that can be heard by humans is 20 hertz. The maximum pressure P produced from a sound with a frequency of 20 hertz is 0.02 millipascal. Write and graph a sine model that gives the pressure P as a function of the time t(in seconds).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-11.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 11.1\" width=\"567\" height=\"550\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-11.1.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-11.1-300x291.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-11.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 11.2\" width=\"395\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-11.2.png 395w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-11.2-300x197.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA middle-A tuning fork vibrates with a frequency f of 440 hertz (cycles per second). You strike a middle-A tuning fork with a force that produces a maximum pressure of 5 pascals. Write and graph a sine model that gives the pressure Pas a function of the time t (in seconds).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 6\" width=\"274\" height=\"198\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201316, write a function for the sinusoid.<\/strong><br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39688\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 7\" width=\"279\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 13\" width=\"582\" height=\"656\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-13.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-13-266x300.png 266w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-8.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 8\" width=\"290\" height=\"128\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 9\" width=\"290\" height=\"136\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 15\" width=\"574\" height=\"713\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-15.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-15-242x300.png 242w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-10.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 10\" width=\"282\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the amplitude of a sinusoid with a maximum point at (2, 10) and a minimum point at (4, \u22126).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 11\" width=\"309\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-11.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-11-300x130.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 17\" width=\"567\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-17.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-17-300x60.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the vertical shift of a sinusoid with a maximum point at (3, \u22122) and a minimum point at (7, \u22128).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-12.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 12\" width=\"315\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-12.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-12-300x129.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nOne of the largest sewing machines in the world has a flywheel (which turns as the machine sews) that is 5 feet in diameter. The highest point of the handle at the edge of the flywheel is 9 feet above the ground, and the lowest point is 4 feet. The wheel makes a complete turn every 2 seconds. Write a model for the height h(in feet) of the handle as a function of the time t(in seconds) given that the handle is at its lowest point when t = 0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 19\" width=\"561\" height=\"721\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-19.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-19-233x300.png 233w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe Great LaxeyWheel, located on the Isle of Man, is the largest working water wheel in the world. The highest point of a bucket on the wheel is 70.5 feet above the viewing platform, and the lowest point is 2 feet below the viewing platform. The wheel makes a complete turn every 24 seconds. Write a model for the height h(in feet) of the bucket as a function of time t (in seconds) given that the bucket is at its lowest point when t = 0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 13\" width=\"273\" height=\"205\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 21 and 22, the time t is measured in months, where t = 1 represents January. Write a model that gives the average monthly high temperature D as a function of t and interpret the period of the graph.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-14.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 14\" width=\"291\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 21\" width=\"589\" height=\"405\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-21.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-21-300x206.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-15-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 15\" width=\"298\" height=\"144\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA circuit has an alternating voltage of 100 volts that peaks every 0.5 second. Write a sinusoidal model for the voltage Vas a function of the time t (in seconds).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-16.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 16\" width=\"228\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 23\" width=\"589\" height=\"645\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-23.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-23-274x300.png 274w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nThe graph shows the average daily temperature of Lexington, Kentucky. The average daily temperature of Louisville, Kentucky, is modeled by y =\u221222 cos \\(\\frac{\\pi}{6}\\)t + 57, where y is the temperature (in degrees Fahrenheit) and t is the number of months since January 1. Which city has the greater average daily temperature? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-17.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 17\" width=\"253\" height=\"164\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nThe table shows the numbers of employees N (in thousands) at a sporting goods company each year for 11 years. The time t is measured in years, with t = 1 representing the first year.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-18.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 18\" width=\"296\" height=\"130\" \/><br \/>\na. Use sinusoidal regression to find a model that gives N as a function of t.<br \/>\nb. Predict the number of employees at the company in the 12th year.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 25\" width=\"571\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-25.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-25-300x79.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe figure shows a tangent line drawn to the graph of the function y = sin x. At several points on the graph, draw a tangent line to the graph and estimate its slope. Then plot the points (x, m), where m is the slope of the tangent line. What can you conclude?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 19\" width=\"315\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-19.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-19-300x140.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>REASONING<\/strong><br \/>\nDetermine whether you would use a sine or cosine function to model each sinusoid with the y-intercept described. Explain your reasoning.<br \/>\na. The y-intercept occurs at the maximum value of the function.<br \/>\nb. The y-intercept occurs at the minimum value of the function.<br \/>\nc. The y-intercept occurs halfway between the maximum and minimum values of the function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 27\" width=\"589\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-27.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-27-300x61.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nWhat is the frequency of the function whose graph is shown? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-20.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 20\" width=\"299\" height=\"140\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nDuring one cycle, a sinusoid has a minimum at (\\(\\frac{\\pi}{2}\\), 3 ) and a maximum at (\\(\\frac{\\pi}{4}\\), 8 ). Write a sine function and a cosine function for the sinusoid. Use a graphing calculator to verify that your answers are correct.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 29\" width=\"569\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-29.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-29-300x130.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that a function with a frequency of 2 has a greater period than a function with a frequency of \\(\\frac{1}{2}\\). Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe low tide at a port is 3.5 feet and occurs at midnight. After 6 hours, the port is at high tide, which is 16.5 feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 21\" width=\"280\" height=\"138\" \/><br \/>\na. Write a sinusoidal model that gives the tide depth d(in feet) as a function of the time t(in hours). Let t = 0 represent midnight.<br \/>\nb. Find all the times when low and high tides occur in a 24-hour period.<br \/>\nc. Explain how the graph of the function you wrote in part (a) is related to a graph that shows the tide depth d at the port t hours after 3:00 A.M.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 31\" width=\"552\" height=\"635\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-31.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-31-261x300.png 261w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 32.<br \/>\n\\(\\frac{17}{\\sqrt{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n\\(\\frac{3}{\\sqrt{6}-2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 33\" width=\"278\" height=\"216\" \/><\/p>\n<p>Question 34.<br \/>\n\\(\\frac{8}{\\sqrt{10}+3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n\\(\\frac{13}{\\sqrt{3}+\\sqrt{11}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 35\" width=\"371\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-35.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-35-300x175.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p><strong>Expand the logarithmic expression.<\/strong><br \/>\nQuestion 36.<br \/>\nlog<sub>8<\/sub>\\(\\frac{x}{7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nln 2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 37\" width=\"199\" height=\"27\" \/><\/p>\n<p>Question 38.<br \/>\nlog<sub>3<\/sub> 5x<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nln \\(\\frac{4 x^{6}}{y}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-9-Trigonometric-Ratios-and-Functions-9.6-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions 9.6 a 39\" width=\"292\" height=\"129\" \/><\/p>\n<h3><a id=\"Lesson_9.7_Using_Trigonometric_Identities\"><\/a>Lesson 9.7 Using Trigonometric Identities<\/h3>\n<p><strong>Essential Question<\/strong> How can you verify a trigonometric identity?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing a Trigonometric Identity<br \/>\nWork with a partner. In the figure, the point (x, y) is on a circle of radius c with center at the origin.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 1\" width=\"203\" height=\"195\" \/><br \/>\na. Write an equation that relates a, b, and c.<br \/>\nb. Write expressions for the sine and cosine ratios of angle \u03b8.<br \/>\nc. Use the results from parts (a) and (b) to find the sum of sin<sup>2<\/sup>\u03b8 and cos<sup>2<\/sup>\u03b8. What do you observe?<br \/>\nd. Complete the table to verify that the identity you wrote in part (c) is valid for angles (of your choice) in each of the four quadrants.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39705\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 2\" width=\"493\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-2.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-2-300x89.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing Other Trigonometric Identities<br \/>\nWork with a partner. The trigonometric identity you derived in Exploration 1 is called a Pythagorean identity. There are two other Pythagorean identities. To derive them, recall the four relationships:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 3\" width=\"599\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-3.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-3-300x78.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><br \/>\na. Divide each side of the Pythagorean identity you derived in Exploration 1 by cos<sup>2<\/sup>\u03b8 and simplify. What do you observe?<br \/>\nb. Divide each side of the Pythagorean identity you derived in Exploration 1 by sin<sup>2<\/sup>\u03b8 and simplify. What do you observe?<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you verify a trigonometric identity?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nIs sin \u03b8 = cos \u03b8 a trigonometric identity? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nGive some examples of trigonometric identities that are different than those in Explorations 1 and 2.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nGiven that cos \u03b8 = \\(\\frac{1}{6}\\) and 0 &lt; \u03b8 &lt; \\(\\frac{\\pi}{2}\\), find the values of the other five trigonometric functions of \u03b8.<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 2.<br \/>\nsin x cot x sec x<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ncos \u03b8 \u2212 cos \u03b8 sin<sup>2<\/sup>\u03b8<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{\\tan x \\csc x}{\\sec x}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Verify the identity.<\/strong><br \/>\nQuestion 5.<br \/>\ncot(\u2212\u03b8) =\u2212cot \u03b8<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\ncsc<sup>2<\/sup>x(1 \u2212 sin2x) = cot<sup>2<\/sup>x<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ncos x csc x tan x = 1<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n(tan<sup>2<\/sup>x + 1)(cos<sup>2<\/sup>x\u2212 1) = \u2212tan<sup>2<\/sup>x<br \/>\nAnswer:<\/p>\n<h3><a id=\"Using_Trigonometric_Identities_9.7_Exercises\"><\/a>Using Trigonometric Identities 9.7 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe the difference between a trigonometric identity and a trigonometric equation.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 1\" width=\"579\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-1-300x44.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to use trigonometric identities to determine whether sec(\u2212\u03b8) = sec \u03b8 or sec(\u2212\u03b8) = \u2212sec \u03b8.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, find the values of the other five trigonometric functions of \u03b8.<\/strong><br \/>\nQuestion 3.<br \/>\nsin\u03b8 = \\(\\frac{1}{3}\\), 0 &lt; \u03b8 &lt; \\(\\frac{\\pi}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 3\" width=\"581\" height=\"590\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-3.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-3-295x300.png 295w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 4.<br \/>\nsin \u03b8 = \u2212\\(\\frac{7}{10}\\), \u03c0 &lt; \u03b8 &lt; \\(\\frac{3 \\pi}{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\ntan\u03b8 = \u2212\\(\\frac{3}{7}\\), \\(\\frac{\\pi}{2}\\) &lt; \u03b8 &lt; \u03c0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-5.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 5.1\" width=\"560\" height=\"578\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-5.1.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-5.1-291x300.png 291w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-5.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 5.2\" width=\"331\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-5.2.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-5.2-300x182.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><\/p>\n<p>Question 6.<br \/>\ncot \u03b8 = \u2212\\(\\frac{2}{5}\\), \\(\\frac{\\pi}{2}\\) &lt; \u03b8 &lt; \u03c0<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ncos \u03b8 = \u2212\\(\\frac{5}{6}\\), \u03c0 &lt; \u03b8 &lt; \\(\\frac{3 \\pi}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-7.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 7.1\" width=\"556\" height=\"619\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-7.1.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-7.1-269x300.png 269w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-7.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 7.2\" width=\"360\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-7.2.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-7.2-300x150.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><\/p>\n<p>Question 8.<br \/>\nsec \u03b8 = \\(\\frac{9}{4}\\), \\(\\frac{3 \\pi}{2}\\) &lt; \u03b8 &lt; 2\u03c0<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ncot \u03b8 = \u22123, \\(\\frac{3 \\pi}{2}\\) &lt; \u03b8 &lt; 2\u03c0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 9\" width=\"572\" height=\"570\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-9.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-9-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-9-150x150.png 150w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 10.<br \/>\ncsc \u03b8 = \u2212\\(\\frac{5}{3}\\), \u03c0 &lt; \u03b8 &lt; \\(\\frac{3 \\pi}{2}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 11\u201320, simplify the expression.<\/strong><br \/>\nQuestion 11.<br \/>\nsin x cot x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 11\" width=\"276\" height=\"83\" \/><\/p>\n<p>Question 12.<br \/>\ncos \u03b8 (1 + tan<sup>2<\/sup>\u03b8)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{\\sin (-\\theta)}{\\cos (-\\theta)}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 13\" width=\"188\" height=\"91\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\frac{\\cos ^{2} x}{\\cot ^{2} x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{\\cos \\left(\\frac{\\pi}{2}-x\\right)}{\\csc x} \\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 15\" width=\"211\" height=\"142\" \/><\/p>\n<p>Question 16.<br \/>\nsin(\\(\\frac{\\pi}{2}\\) &#8211; \u03b8) sec \u03b8<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{\\csc ^{2} x-\\cot ^{2} x}{\\sin (-x) \\cot x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 17\" width=\"330\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-17.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-17-300x281.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{\\cos ^{2} x \\tan ^{2}(-x)-1}{\\cos ^{2} x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{\\cos \\left(\\frac{\\pi}{2}-\\theta\\right)}{\\csc \\theta}\\) + cos<sup>2<\/sup> \u03b8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 19\" width=\"378\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-19.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-19-300x152.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{\\sec x \\sin x+\\cos \\left(\\frac{\\pi}{2}-x\\right)}{1+\\sec x}\\)<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 21 and 22, describe and correct the error in simplifying the expression.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 4\" width=\"316\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-4.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-4-300x93.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 21\" width=\"560\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-21.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-21-300x77.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 5\" width=\"322\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-5.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-5-300x96.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 23\u201330, verify the identity.<\/strong><br \/>\nQuestion 23.<br \/>\nsin x csc x = 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 23\" width=\"251\" height=\"87\" \/><\/p>\n<p>Question 24.<br \/>\ntan \u03b8 csc \u03b8 cos \u03b8 = 1<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\ncos (\\(\\frac{3 \\pi}{2}\\) \u2212 x)cot x = cos x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 25\" width=\"317\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-25.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-25-300x75.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Question 26.<br \/>\nsin (\\(\\frac{3 \\pi}{2}\\) \u2212 x)tan x = sin x<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n\\(\\frac{\\cos \\left(\\frac{\\pi}{2}-\\theta\\right)+1}{1-\\sin (-\\theta)}\\) = 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 27\" width=\"322\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-27.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-27-300x227.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\frac{\\sin ^{2}(-x)}{\\tan ^{2} x}\\) = cos<sup>2<\/sup> x<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n\\(\\frac{1+\\cos x}{\\sin x}+\\frac{\\sin x}{1+\\cos x}\\) = 2 csc x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 29\" width=\"571\" height=\"492\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-29.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-29-300x258.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 30.<br \/>\n\\(\\frac{\\sin x}{1-\\cos (-x)}\\) = csc x + cot x<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nA function f is odd when f(\u2212x) = \u2212f(x). A function f is even when (\u2212x) = f (x). Which of the six trigonometric functions are odd? Which are even? Justify your answers using identities and graphs.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-31.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 31.1\" width=\"349\" height=\"482\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-31.1.png 349w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-31.1-217x300.png 217w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-31.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 31.2\" width=\"563\" height=\"605\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-31.2.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-31.2-279x300.png 279w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nAs the value of cos \u03b8 increases, what happens to the value of sec \u03b8? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend simplifies an expression and obtains sec x tan x\u2212 sin x. You simplify the same expression and obtain sin x tan2x. Are your answers equivalent? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 33\" width=\"404\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-33.png 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-33-300x194.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe figure shows the unit circle and the angle \u03b8.<br \/>\na. Is sin \u03b8 positive or negative? cos \u03b8? tan \u03b8?<br \/>\nb. In what quadrant does the terminal side of \u2212\u03b8 lie?<br \/>\nc. Is sin(\u2212\u03b8) positive or negative? cos(\u2212\u03b8)? tan(\u2212\u03b8)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 6\" width=\"160\" height=\"157\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA vertical gnomon(the part of a sundial that projects a shadow) has height h. The length s of the shadow cast by the gnomon when the angle of the Sun above the horizon is \u03b8 can be modeled by the equation below. Show that the equation below is equivalent to s = h cot \u03b8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 7\" width=\"351\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-7.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-7-300x156.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 35\" width=\"192\" height=\"147\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nExplain how you can use a trigonometric identity to find all the values of x for which sin x = cos x.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nStatic friction is the amount of force necessary to keep a stationary object on a flat surface from moving. Suppose a book weighing W pounds is lying on a ramp inclined at an angle \u03b8. The coefficient of static friction u for the book can be found using the equation uW cos \u03b8 = W sin \u03b8.<br \/>\na. Solve the equation for u and simplify the result.<br \/>\nb. Use the equation from part (a) to determine what happens to the value of u as the angle \u03b8 increases from 0\u00b0 to 90\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 37\" width=\"563\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-37.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-37-300x118.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nWhen light traveling in a medium (such as air) strikes the surface of a second medium (such as water) at an angle \u03b8<sub>1<\/sub>, the light begins to travel at a different angle \u03b8<sub>2<\/sub>. This change of direction is defined by Snell\u2019s law, n<sub>1<\/sub> sin \u03b8<sub>1<\/sub> = n<sub>2<\/sub> sin \u03b8<sub>2<\/sub>, where n<sub>1<\/sub> and n<sub>2<\/sub> are the indices of refraction for the two mediums. Snell\u2019s law can be derived from the equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-8.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 8\" width=\"329\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-8.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-8-300x132.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\na. Simplify the equation to derive Snell\u2019s law.<br \/>\nb. What is the value of n1 when \u03b8<sub>1<\/sub> = 55\u00b0, \u03b8<sub>2<\/sub> = 35\u00b0, and n<sub>2<\/sub> = 2?<br \/>\nc. If \u03b8<sub>1<\/sub> = \u03b8<sub>2<\/sub>, then what must be true about the values of n<sub>1<\/sub> and n<sub>2<\/sub>? Explain when this situation would occur.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how transformations of the graph of the parent function f(x) = sin x support the cofunction identity sin (\\(\\frac{\\pi}{2}\\) \u2212 \u03b8) = cos \u03b8.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 39\" width=\"521\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-39.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-39-300x71.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nVerify each identity.<br \/>\na. ln \u2223sec \u03b8\u2223= \u2212ln \u2223cos \u03b8\u2223<br \/>\nb. ln \u2223tan \u03b8\u2223= ln \u2223sin \u03b8\u2223\u2212 ln \u2223cos \u03b8\u2223<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Find the value of x for the right triangle.<\/strong><br \/>\nQuestion 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 9\" width=\"113\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 41\" width=\"574\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-41.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-41-300x133.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-10.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 10\" width=\"88\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 11\" width=\"162\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions 9.7 a 43\" width=\"515\" height=\"418\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-43.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions-9.7-a-43-300x243.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<h3><a id=\"Lesson_9.8_Using_Sum_and_Difference_Formulas\"><\/a>Lesson 9.8 Using Sum and Difference Formulas<\/h3>\n<p><strong>Essential Question<\/strong> How can you evaluate trigonometric functions of the sum or difference of two angles?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Deriving a Difference Formula<br \/>\nWork with a partner.<br \/>\na. Explain why the two triangles shown are congruent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 1\" width=\"521\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-1.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-1-300x103.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><br \/>\nb. Use the Distance Formula to write an expression for d in the first unit circle.<br \/>\nc. Use the Distance Formula to write an expression for d in the second unit circle.<br \/>\nd. Write an equation that relates the expressions in parts (b) and (c). Then simplify this equation to obtain a formula for cos(a \u2212 b).<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Deriving a Sum Formula<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 2\" width=\"227\" height=\"175\" \/><br \/>\nWork with a partner. Use the difference formula you derived in Exploration 1 to write a formula for cos(a+b) in terms of sine and cosine of a and b. Hint: Use the fact that cos(a+b) = cos[a \u2212 (\u2212b)].<\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Deriving Difference and Sum Formulas<br \/>\nWork with a partner. Use the formulas you derived in Explorations 1 and 2 to write formulas for sin(a \u2212 b) and sin(a + b) in terms of sine and cosine of a and b. Hint: Use the cofunction identities sin (\\(\\frac{\\pi}{2}\\) \u2212 a)= cos a and cos (\\(\\frac{\\pi}{2}\\) \u2212 a)= sin a and the fact that<br \/>\ncos [(\\(\\frac{\\pi}{2}\\) \u2212 a) + b ]= sin(a \u2212 b) and sin(a+b) = sin[a \u2212 (\u2212b)].<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you evaluate trigonometric functions of the sum or difference of two angles?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\na. Find the exact values of sin 75\u00b0 and cos 75\u00b0 using sum formulas. Explain your reasoning.<br \/>\nb. Find the exact values of sin 75\u00b0 and cos 75\u00b0 using difference formulas. Compare your answers to those in part (a).<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Find the exact value of the expression.<\/strong><br \/>\nQuestion 1.<br \/>\nsin 105\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ncos 15\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ntan \\(\\frac{5 \\pi}{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ncos \\(\\frac{\\pi}{12}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nFind sin(a\u2212b) given that sin a = \\(\\frac{8}{17}\\) with 0 &lt; a &lt; \\(\\frac{\\pi}{2}\\) and cos b = \u2212\\(\\frac{24}{25}\\) with \u03c0 &lt; b &lt; \\(\\frac{3 \\pi}{2}\\) .<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 6.<br \/>\nsin(x + \u03c0)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ncos(x \u2212 2\u03c0)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ntan(x \u2212 \u03c0)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nSolve sin (\\(\\frac{\\pi}{4}\\) \u2212 x)\u2212 sin (x + \\(\\frac{\\pi}{4}\\))= 1 for 0 \u2264 x &lt; 2\u03c0.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Using_Sum_and_Difference_Formulas_9.8_Exercises\"><\/a>Using Sum and Difference Formulas 9.8 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nWrite the expression cos 130\u00b0 cos 40\u00b0\u2212 sin 130\u00b0 sin 40\u00b0 as the cosine of an angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 1\" width=\"277\" height=\"29\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to evaluate tan 75\u00b0 using either the sum or difference formula for tangent.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, find the exact value of the expression.<\/strong><br \/>\nQuestion 3.<br \/>\ntan(\u221215\u00b0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 3\" width=\"320\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-3.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-3-300x232.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<p>Question 4.<br \/>\ntan 195\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nsin \\(\\frac{23 \\pi}{12}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 5\" width=\"388\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-5.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-5-300x182.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 6.<br \/>\nsin(\u2212165\u00b0)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ncos 105\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 7\" width=\"415\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-7.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-7-300x134.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p>\n<p>Question 8.<br \/>\ncos \\(\\frac{11 \\pi}{12}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ntan \\(\\frac{17 \\pi}{12}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 9\" width=\"286\" height=\"293\" \/><\/p>\n<p>Question 10.<br \/>\nsin (\u2212\\(\\frac{7 \\pi}{12}\\))<br \/>\nAnswer:<\/p>\n<p>In Exercises 11\u201316, evaluate the expression given that cos a = \\(\\frac{4}{5}\\) with 0 &lt; a &lt; \\(\\frac{\\pi}{2}\\) and sin b = &#8211;\\(\\frac{15}{17}\\) with \\(\\frac{3 \\pi}{2}\\) &lt; b &lt; 2\u03c0.<br \/>\nQuestion 11.<br \/>\nsin(a + b)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-11.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 11.1\" width=\"560\" height=\"612\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-11.1.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-11.1-275x300.png 275w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-11.2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 11.2\" width=\"452\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-11.2.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-11.2-300x109.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 12.<br \/>\nsin(a \u2212 b)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\ncos(a \u2212 b)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-13.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 13.1\" width=\"557\" height=\"604\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-13.1.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-13.1-277x300.png 277w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-13.2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 13.2\" width=\"538\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-13.2.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-13.2-300x81.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 14.<br \/>\ncos(a + b)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ntan(a + b)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-15.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 15.1\" width=\"570\" height=\"621\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-15.1.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-15.1-275x300.png 275w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-15.2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 15.2\" width=\"481\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-15.2.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-15.2-300x170.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 16.<br \/>\ntan(a \u2212 b)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 17\u201322, simplify the expression.<\/strong><br \/>\nQuestion 17.<br \/>\ntan(x + \u03c0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-17.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 17\" width=\"306\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-17.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-17-300x146.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/p>\n<p>Question 18.<br \/>\ncos (x \u2212 \\(\\frac{\\pi}{2}\\))<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\ncos(x + 2\u03c0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-19.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 19\" width=\"416\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-19.png 416w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-19-300x70.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Question 20.<br \/>\ntan(x \u2212 2\u03c0)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nsin (x \u2212 \\(\\frac{3 \\pi}{2}\\))<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-21.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 21\" width=\"415\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-21.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-21-300x88.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p>\n<p>Question 22.<br \/>\ntan (x + \\(\\frac{\\pi}{2}\\))<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 23 and 24, describe and correct the error in simplifying the expression.<br \/>\nQuestion 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 3\" width=\"316\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-3.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-3-300x144.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-23.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 23\" width=\"552\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-23.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-23-300x120.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-4.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 4\" width=\"318\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-4.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-4-300x143.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nWhat are the solutions of the equation 2 sin x \u2212 1 = 0 for 0 \u2264 x &lt; 2\u03c0?<br \/>\nA. \\(\\frac{\\pi}{3}\\)<br \/>\nB. \\(\\frac{\\pi}{6}\\)<br \/>\nC. \\(\\frac{2 \\pi}{3}\\)<br \/>\nD. \\(\\frac{5 \\pi}{6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-25.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 25\" width=\"430\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-25.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-25-300x37.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/p>\n<p>Question 26.<br \/>\nWhat are the solutions of the equation tan x + 1 = 0 for 0 \u2264 x &lt; 2\u03c0?<br \/>\nA. \\(\\frac{\\pi}{4}\\)<br \/>\nB. \\(\\frac{3 \\pi}{4}\\)<br \/>\nC. \\(\\frac{5 \\pi}{4}\\)<br \/>\nD. \\(\\frac{7 \\pi}{4}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 27\u201332, solve the equation for 0 \u2264 x &lt; 2\u03c0.<\/strong><br \/>\nQuestion 27.<br \/>\nsin (x + \\(\\frac{\\pi}{2}\\)) = \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-27.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 27\" width=\"562\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-27.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-27-300x147.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 28.<br \/>\ntan (x \u2212 \\(\\frac{\\pi}{4}\\)) = 0<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\ncos (x +\\(\\frac{\\pi}{6}\\)) \u2212 cos (x \u2212\\(\\frac{\\pi}{6}\\)) = 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-29.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 29\" width=\"558\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-29.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-29-300x157.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 30.<br \/>\nsin (x + \\(\\frac{\\pi}{4}\\)) + sin (x \u2212 \\(\\frac{\\pi}{4}\\)) = 0<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\ntan(x + \u03c0) \u2212 tan(\u03c0 \u2212 x) = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-31.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 31\" width=\"568\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-31.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-31-300x127.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 32.<br \/>\nsin(x + \u03c0) + cos(x + \u03c0) = 0<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nDerive the cofunction identity sin (\\(\\frac{\\pi}{2}\\) \u2212 \u03b8)= cos \u03b8 using the difference formula for sine.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-33.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 33\" width=\"385\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-33.png 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-33-300x90.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims it is possible to use the difference formula for tangent to derive the cofunction identity tan (\\(\\frac{\\pi}{2}\\) \u2212 \u03b8) = cot \u03b8. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA photographer is at a height h taking aerial photographs with a 35-millimeter camera. The ratio of the image length WQ to the length NA of the actual object is given by the formula<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 5\" width=\"333\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-5.png 333w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-5-300x131.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><br \/>\nwhere \u03b8 is the angle between the vertical line perpendicular to the ground and the line from the camera to point A and t is the tilt angle of the film. When t = 45\u00b0, show that the formula can be rewritten as \\(\\frac{W Q}{N A}=\\frac{70}{h(1+\\tan \\theta)}\\).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-35.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 35\" width=\"366\" height=\"544\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-35.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-35-202x300.png 202w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nWhen a wave travels through a taut string, the displacement y of each point on the string depends on the time t and the point\u2019s position x. The equation of a standing wave can be obtained by adding the displacements of two waves traveling in opposite directions. Suppose a standing wave can be modeled by the formula<br \/>\ny = A cos (\\(\\frac{2 \\pi t}{3}-\\frac{2 \\pi x}{5}\\)) + A cos (\\(\\frac{2 \\pi t}{3}+\\frac{2 \\pi x}{5}\\)) .When t= 1, show that the formula can be rewritten as y = \u2212A cos \\(\\frac{2 \\pi x}{5}\\).<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe busy signal on a touch-tone phone is a combination of two tones with frequencies of 480 hertz and 620 hertz. The individual tones can be modeled by the equations:<br \/>\n480 hertz: y<sub>1<\/sub> = cos 960\u03c0t<br \/>\n620 hertz: y<sub>2<\/sub> = cos 1240\u03c0t<br \/>\nThe sound of the busy signal can be modeled by y<sub>1<\/sub> + y<sub>2<\/sub>. Show that y<sub>1<\/sub> + y<sub>2<\/sub> = 2 cos 1100\u03c0t cos 140\u03c0t.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-37.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 37\" width=\"544\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-37.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-37-300x111.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nExplain how to use the figure to solve the equation sin (x + \\(\\frac{\\pi}{4}\\)) \u2212 sin (\\(\\frac{\\pi}{4}\\) \u2212 x) = 0 for 0 \u2264 x &lt; 2\u03c0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-6.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 6\" width=\"238\" height=\"161\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe figure shows the acute angle of intersection, \u03b8<sub>2<\/sub> \u2212 \u03b8<sub>1<\/sub>, of two lines with slopes m<sub>1<\/sub> and m<sub>2<\/sub>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 7\" width=\"239\" height=\"188\" \/><br \/>\na. Use the difference formula for tangent to write an equation for tan (\u03b8<sub>2<\/sub> \u2212 \u03b8<sub>1<\/sub>) in terms of m<sub>1<\/sub> and m<sub>2<\/sub>.<br \/>\nb. Use the equation from part (a) to find the acute angle of intersection of the lines y = x\u2212 1 and y = \\(\\left(\\frac{1}{\\sqrt{3}-2}\\right)\\)x + \\(\\frac{4-\\sqrt{3}}{2-\\sqrt{3}}\\).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-39.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 39.1\" width=\"504\" height=\"578\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-39.1.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-39.1-262x300.png 262w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-39.2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 39.2\" width=\"354\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-39.2.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-39.2-300x226.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nRewrite each function. Justify your answers.<br \/>\na. Write sin 3x as a function of sin x.<br \/>\nb. Write cos 3x as a function of cos x.<br \/>\nc. Write tan 3x as a function of tan x.<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution(s).<\/strong><br \/>\nQuestion 41.<br \/>\n1 \u2212 \\(\\frac{9}{x-2}\\) = \u2212\\(\\frac{7}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-41.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 41\" width=\"521\" height=\"317\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-41.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-41-300x183.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 42.<br \/>\n\\(\\frac{12}{x}\\) + \\(\\frac{3}{4}\\) = \\(\\frac{8}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{2 x-3}{x+1}\\) = \\(\\frac{10}{x^{2}-1}\\) + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-43.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 43.1\" width=\"560\" height=\"567\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-43.1.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-43.1-296x300.png 296w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-43.2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 a 43.2\" width=\"367\" height=\"584\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-43.2.png 367w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-a-43.2-189x300.png 189w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<h3><a id=\"Trigonometric_Ratios_and_Functions_Performance_Task:_Lightening_the_Load\"><\/a>Trigonometric Ratios and Functions Performance Task: Lightening the Load<\/h3>\n<p><strong>9.5\u20139.8 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\nfrequency, p. 506<br \/>\nsinusoid, p. 507<br \/>\ntrigonometric identity, p. 514<\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 9.5<br \/>\nCharacteristics of y = tan x and y = cot x, p. 498<br \/>\nPeriod and Vertical Asymptotes of y = a tan bx and y = a cot bx, p. 499<br \/>\nCharacteristics of y = sec x and y = csc x, p. 500<\/p>\n<p>Section 9.6<br \/>\nFrequency, p. 506<br \/>\nWriting Trigonometric Functions, p. 507<br \/>\nUsing Technology to Find Trigonometric Models, p. 509<\/p>\n<p>Section 9.7<br \/>\nFundamental Trigonometric Identities, p. 514<\/p>\n<p>Section 9.8<br \/>\nSum and Difference Formulas, p. 520<br \/>\nTrigonometric Equations and Real-Life Formulas, p. 522<\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nExplain why the relationship between \u03b8 and d makes sense in the context of the situation in Exercise 43 on page 503.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nHow can you use definitions to relate the slope of a line with the tangent of an angle in Exercise 39 on page 524?<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task: Lightening the Load<\/strong><\/p>\n<p>You need to move a heavy table across the room. What is the easiest way to move it? Should you push it? Should you tie a rope around one leg of the table and pull it? How can trigonometry help you make the right decision?<br \/>\nTo explore the answers to these questions and more, go to BigIdeasMath.com.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-8.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions 9.8 8\" width=\"358\" height=\"291\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-8.png 358w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-9.8-8-300x244.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/p>\n<h3><a id=\"Trigonometric_Ratios_and_Functions_Chapter_Review\"><\/a>Trigonometric Ratios and Functions Chapter Review<\/h3>\n<p><strong>9.1 Right Triangle Trigonometry (pp. 461\u2212468)<\/strong><\/p>\n<p>Question 1.<br \/>\nIn a right triangle, \u03b8 is an acute angle and cos \u03b8 = \\(\\frac{6}{11}\\). Evaluate the other five trigonometric functions of \u03b8.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nThe shadow of a tree measures 25 feet from its base. The angle of elevation to the Sun is 31\u00b0. How tall is the tree?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions cr 2\" width=\"201\" height=\"150\" \/><br \/>\nAnswer:<\/p>\n<p><strong>9.2 Angles and Radian Measure (pp. 469\u2212476)<\/strong><\/p>\n<p>Question 3.<br \/>\nFind one positive angle and one negative angle that are coterminal with 382\u00b0.<br \/>\nAnswer:<\/p>\n<p>Convert the degree measure to radians or the radian measure to degrees.<br \/>\nQuestion 4.<br \/>\n30\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n225\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3 \\pi}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{5 \\pi}{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nA sprinkler system on a farm rotates 140\u00b0and sprays water up to 35 meters. Draw a diagram that shows the region that can be irrigated with the sprinkler. Then find the area of the region.<br \/>\nAnswer:<\/p>\n<p><strong>9.3 Trigonometric Functions of Any Angle (pp. 477\u2212484)<\/strong><\/p>\n<p><strong>Evaluate the six trigonometric functions of \u03b8.<\/strong><br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions cr 9\" width=\"166\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-10.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions cr 10\" width=\"181\" height=\"162\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions cr 11\" width=\"168\" height=\"164\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Evaluate the function without using a calculator.<\/strong><br \/>\nQuestion 12.<br \/>\ntan 330\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nsec(\u2212405\u00b0)<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nsin \\(\\frac{13 \\pi}{6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nsec \\(\\frac{11 \\pi}{3}\\)<br \/>\nAnswer:<\/p>\n<p><strong>9.4 Graphing Sine and Cosine Functions (pp. 485\u2212494)<\/strong><\/p>\n<p>Identify the amplitude and period of the function. Then graph the function and describe the graph of g as a transformation of the graph of the parent function.<br \/>\nQuestion 16.<br \/>\ng(x) = 8 cos x<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\ng(x) = 6 sin \u03c0x<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\ng(x) = \\(\\frac{1}{4}\\) cos 4x<br \/>\nAnswer:<\/p>\n<p>Graph the function.<br \/>\nQuestion 19.<br \/>\ng(x) = cos(x + \u03c0) + 2<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\ng(x) = \u2212sin x \u2212 4<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\ng(x) = 2 sin (x + \\(\\frac{\\pi}{2}\\))<br \/>\nAnswer:<\/p>\n<p><strong>9.5 Graphing Other Trigonometric Functions (pp. 497\u2212504)<\/strong><\/p>\n<p>Graph one period of the function. Describe the graph of g as a transformation of the graph of its parent function.<br \/>\nQuestion 22.<br \/>\ng(x) = tan \\(\\frac{1}{2}\\)x<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\ng(x) = 2 cot x<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\ng(x) = 4 tan 3\u03c0x<br \/>\nAnswer:<\/p>\n<p>Graph the function.<br \/>\nQuestion 25.<br \/>\ng(x) = 5 csc x<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\ng(x) = sec \\(\\frac{1}{2}\\)x<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\ng(x) = 5 sec \u03c0x<br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\ng(x) = \\(\\frac{1}{2}\\) csc \\(\\frac{\\pi}{4}\\)x<br \/>\nAnswer:<\/p>\n<p><strong>9.6 Modeling with Trigonometric Functions (pp. 505\u2212512)<\/strong><\/p>\n<p><strong>Write a function for the sinusoid.<\/strong><br \/>\nQuestion 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-29.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions cr 29\" width=\"228\" height=\"112\" \/><br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-30.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions cr 30\" width=\"219\" height=\"127\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nYou put a reflector on a spoke of your bicycle wheel. The highest point of the reflector is 25 inches above the ground, and the lowest point is 2 inches. The reflector makes 1 revolution per second. Write a model for the height h (in inches) of a reflector as a function of time t (in seconds) given that the reflector is at its lowest point when t = 0.<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\nThe table shows the monthly precipitation P (in inches) for Bismarck, North Dakota, where t = 1 represents January. Write a model that gives P as a function of t and interpret the period of its graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-32.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions cr 32\" width=\"466\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-32.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-cr-32-300x52.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>9.7 Using Trigonometric Identities (pp. 513\u2212518)<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 33.<br \/>\ncot<sup>2<\/sup>x \u2212 cot<sup>2<\/sup>x cos<sup>2<\/sup>x<br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\n\\(\\frac{(\\sec x+1)(\\sec x-1)}{\\tan x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nsin (\\(\\frac{\\pi}{2}\\) \u2212 x)tan x<br \/>\nAnswer:<\/p>\n<p><strong>Verify the identity.<\/strong><br \/>\nQuestion 36.<br \/>\n\\(\\frac{\\cos x \\sec x}{1+\\tan ^{2} x}\\) = cos<sup>2<\/sup>x<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ntan (\\(\\frac{\\pi}{2}\\) \u2212 x)cot x = csc<sup>2<\/sup>x \u2212 1<br \/>\nAnswer:<\/p>\n<p><strong>9.8 Using Sum and Difference Formulas (pp. 519\u2212524)<\/strong><\/p>\n<p><strong>Find the exact value of the expression.<\/strong><br \/>\nQuestion 38.<br \/>\nsin 75\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\ntan(\u221215\u00b0)<br \/>\nAnswer:<\/p>\n<p>Question 40.<br \/>\ncos \\(\\frac{\\pi}{12}\\)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nFind tan(a + b), given that tan a = \\(\\frac{1}{4}\\) with \u03c0 &lt; a &lt; \\(\\frac{3 \\pi}{2}\\) and tan b = \\(\\frac{3}{7}\\) with 0 &lt; b &lt; \\(\\frac{\\pi}{2}\\) .<br \/>\nAnswer:<\/p>\n<p>Solve the equation for 0 \u2264 x &lt; 2\u03c0.<br \/>\nQuestion 42.<br \/>\ncos (x + \\(\\frac{3 \\pi}{4}\\)) + cos (x \u2212 \\(\\frac{3 \\pi}{4}\\)) = 1<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\ntan(x + \u03c0) + cos (x + \\(\\frac{\\pi}{2}\\))= 0<br \/>\nAnswer:<\/p>\n<h3><a id=\"Trigonometric_Ratios_and_Functions_Chapter_Test\"><\/a>Trigonometric Ratios and Functions Chapter Test<\/h3>\n<p><strong>Verify the identity.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{\\cos ^{2} x+\\sin ^{2} x}{1+\\tan ^{2} x}\\) = cos<sup>2<\/sup>x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1+\\sin x}{\\cos x}+\\frac{\\cos x}{1+\\sin x}\\) = 2 sec x<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ncos (x + \\(\\frac{3 \\pi}{2}\\)) = sin x<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nEvaluate sec(\u2212300\u00b0) without using a calculator.<br \/>\nAnswer:<\/p>\n<p>Write a function for the sinusoid.<br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-ct-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions ct 5\" width=\"241\" height=\"143\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-ct-6.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions ct 6\" width=\"230\" height=\"153\" \/><br \/>\nAnswer:<\/p>\n<p>Graph the function. Then describe the graph of g as a transformation of the graph of its parent function.<br \/>\nQuestion 7.<br \/>\ng(x) = \u22124 tan 2x<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ng(x) = \u22122 cos \\(\\frac{1}{3}\\)x + 3<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ng(x) = 3 csc \u03c0x<br \/>\nAnswer:<\/p>\n<p>Convert the degree measure to radians or the radian measure to degrees. Then find one positive angle and one negative angle that are coterminal with the given angle.<br \/>\nQuestion 10.<br \/>\n\u221250\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{4 \\pi}{5}\\)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{8 \\pi}{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nFind the arc length and area of a sector with radius r = 13 inches and central angle \u03b8 = 40\u00b0.<br \/>\nAnswer:<\/p>\n<p>Evaluate the six trigonometric functions of the angle \u03b8.<br \/>\nQuestion 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-ct-14.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions ct 14\" width=\"169\" height=\"136\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-ct-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions ct 15\" width=\"174\" height=\"155\" \/><br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nIn which quadrant does the terminal side of \u03b8 lie when cos \u03b8 &lt; 0 and tan \u03b8 &gt; 0? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nHow tall is the building? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-ct-17.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions ct 17\" width=\"201\" height=\"130\" \/><br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nThe table shows the average daily high temperatures T (in degrees Fahrenheit) in Baltimore, Maryland, where m= 1 represents January. Write a model that gives T as a function of m and interpret the period of its graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-ct-18.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 9 Trigonometric Ratios and Functions ct 18\" width=\"471\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-ct-18.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-9-Trigonometric-Ratios-and-Functions-ct-18-300x49.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Trigonometric_Ratios_and_Functions_Cumulative_Assessment\"><\/a>Trigonometric Ratios and Functions Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nWhich expressions are equivalent to 1?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions ca 1\" width=\"574\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-1-300x37.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nWhich rational expression represents the ratio of the perimeter to the area of the playground shown in the diagram?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-2.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions ca 2\" width=\"387\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-2.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-2-300x136.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nThe chart shows the average monthly temperatures (in degrees Fahrenheit) and the gas usages (in cubic feet) of a household for 12 months.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions ca 3\" width=\"386\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-3.png 386w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-3-300x230.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><br \/>\na. Use a graphing calculator to find trigonometric models for the average temperature y<sub>1<\/sub> as a function of time and the gas usage y<sub>2<\/sub> (in thousands of cubic feet) as a function of time. Let t = 1 represent January.<br \/>\nb. Graph the two regression equations in the same coordinate plane on your graphing calculator. Describe the relationship between the graphs.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nEvaluate each logarithm using log<sub>2<\/sub> 5 \u2248 2.322 and log<sub>2<\/sub> 3 \u2248 1.585, if necessary. Then order the logarithms by value from least to greatest.<br \/>\na. log 1000<br \/>\nb. log<sub>2<\/sub> 15<br \/>\nc. ln e<br \/>\nd. log<sub>2<\/sub> 9<br \/>\ne. log<sub>2<\/sub>\\(\\frac{5}{3}\\)<br \/>\nf. log<sub>2<\/sub> 1<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWhich function is not represented by the graph?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions ca 5\" width=\"465\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-5.png 465w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-5-300x114.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nComplete each statement with &lt; or &gt; so that each statement is true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-6.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions ca 6\" width=\"436\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-6.png 436w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-6-300x97.png 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nUse the Rational Root Theorem and the graph to find all the real zeros of the function f(x) = 2x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 13x\u2212 6. (HSA-APR.B.3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-9-Trigonometric-Ratios-and-Functions-ca-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 9 Trigonometric Ratios and Functions ca 7\" width=\"163\" height=\"136\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nYour friend claims \u2212210\u00b0 is coterminal with the angle \\(\\frac{5 \\pi}{6}\\). Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nCompany A and Company B offer the same starting annual salary of $20,000. Company A gives a $1000 raise each year. Company B gives a 4% raise each year.<br \/>\na. Write rules giving the salaries an and bn for your nth year of employment at Company A and Company B, respectively. Tell whether the sequence represented by each rule is arithmetic, geometric, or neither.<br \/>\nb. Graph each sequence in the same coordinate plane.<br \/>\nc. Under what conditions would you choose to work for Company B?<br \/>\nd. After 20 years of employment, compare your total earnings.<br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Are you struggling to solve the trigonometric ratios and functions in homework and assignments? Then, check out this Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions and solve your issues within seconds. The perfect way to learn the concepts of ch 9 is by practicing the questions given in the BIM &#8230; <a title=\"Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-9\/\" aria-label=\"More on Big Ideas Math Algebra 2 Answers Chapter 9 Trigonometric Ratios and Functions\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89323,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-9-Trigonometric-Ratios-and-Functions.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/39544"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=39544"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/39544\/revisions"}],"predecessor-version":[{"id":90316,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/39544\/revisions\/90316"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89323"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=39544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=39544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=39544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}