C H A P T E R 5 Analytic Trigonometry

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524 Chapter 5 <strong>Analytic</strong> <strong>Trigonometry</strong> 114. 115. The graph of y1 is a vertical shift of the graph of y2 one unit upward so y1 y2 1. 117. S 6hs where h 2.4 inches, s 0.75 inch, and is the given angle. 3 s 2 3 cos 2 sin , 0 < ≤ 90 (a) For a surface area of 12 square inches, S 62.40.75 3 3 cos 0.752 2 sin 3 cos 10.8 0.84375 12 sin 3 cos 0.84375 sin 1.2. y x 3 4 cos x Zeros: x 1.8431, 2.1758, 3.9903, 8.8935, 9.8820 11 −4 20 Problem Solving for Chapter 5 1. (a) Since Using the solve function of a graphing calculator gives 49.91479 or 59.86118. cos ±1 sin 2 tan sin ± cos cot 1 tan ± 1 sin2 sin sec 1 ± cos cos 1 sin —CONTINUED— sin 1 sin 2 1 1 sin 2 −2 12 (b) Using a graphing calculator yields the following graph: cos 3x 116. y1 cos x If the graph of y2 is reflected in the x-axis and then shifted upward by one unit, it coincides with the graph of y1 . Therefore, , y2 2 sin x2 cos 3x cos x 2 sin x2 1. So, y 1 1 y 2 . 118. y 2 Approximate roots: 3.1395, 2.0000, 1 2 x2 3 sin 2 0.4378, 2.0000 y 2 1 2 x2 3 sin sin 2 cos 2 1 and cos 2 1 sin 2 : We also have the following relationships: 20 0 0 (0.9553, 11.99) cos sin 2 sin tan sin 2 sin cot 2 sin 1 sec sin 2 csc 1 sin 3 4 Using the minimum function yields 0.9553 radians or 54.73466. x x 2 −10 10 7 −7
1. —CONTINUED— 2. 4. (b) cos sin ±1 cos 2 tan csc 1 ± sin sec 1 cos cot 1 ± tan 2n 1 2n 2 cos 2 3. cos cos n cos sin n sin 2 2 ±10 01 0 cos 1 cos 2 2 n 2n 1 Thus, cos for all integers n. 2 0 pt 1 (a) The graph of sin cos ±1 cos2 cos 1 1 cos 2 yields the graph shown in the text and to the right. —CONTINUED— 4 p 1t 30p 2t p 3t p 5t 30p 6t p 1t sin524t p 2t 1 2 sin1048t p 3t 1 3 sin1572t p 5t 1 5 sin2620t p 6t 1 6 sin3144t p 1 p2 p 3 sin 12n 1 6 Problem Solving for Chapter 5 525 We also have the following relationships: sin cos 2 tan csc sec 1 cos cot cos2 cos 1 cos2 cos cos2 sin 1 6 sin 2n sin 1 6 2 12n 6 12n 1 1 Thus, sin for all integers n. 6 2 pt 1 1 1 sin524t 15 sin1048t sin1572t sin2620t 5 sin3144 4 t 3 5 1.4 −0.003 0.003 −1.4 p 5 p 6 1.4 −1.4 y y = p(t) t 0.006
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CHAPTER 5 Analytic Trigonometry Sec
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1. sin x 3 , cos x 1 2 2 tan x si
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19. 22. 24. 26. sinx sin x tan x 2
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53. sin 4 x cos 4 x sin 2 x cos
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74. 75. 76. y 1 sec x csc x tan x
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88. 90. 92. 94. 96. cos 1 sin 2
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Section 5.1 Using Fundamental Ident
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5. cos 2 sin 2 1 sin 2 sin 2
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28. 30. 32. 33. 1 sin y1 siny 1
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43. (a) (b) (c) 45. (a) 47. (b) (c)
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61. 63. 65. 67. 2 3i 26 2 3i 2
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5. 7. 2 sin2 x sin x 1 0 6. csc4
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24. 26. 28. 30. 2 sin 2 x 2 cos x
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40. 42. 44. sin x 2 3 2 x 2 4 2n
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56. 3 tan 2 x 4 tan x 4 0 tan x
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64. (a) f x 2 sin x cos 2x max: 0
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75. —CONTINUED— 76. (a) (b) The
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Section 5.4 Sum and Difference Form
Page 37 and 38: 10. 12. 255 300 45 11. sin 255 sin3
Page 39 and 40: 16. 105 30 135 17. sin30 135 sin
Page 41 and 42: 21. 22. 13 12 3 sin 4 3 cos 4 3 ta
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Page 45 and 46: 53. 54. Let 55. 57. 59. cosarccos x
Page 47 and 48: 69. 70. 71. sin x cos 3 cos x sin
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Page 53 and 54: 97. 99. f x 5x 3 98. f 1 x y 5x
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Page 57 and 58: 15. 17. tan 2x cot x 0 16. 2 tan
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Page 63 and 64: 45. 47. 48. 49. sin 1 sin 8 2 4
Page 65 and 66: 1 cos 6x 55. 2 sin 3x 57. 59. 1
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Page 71 and 72: 111. 112. 114. −2 2 −3 cos 3 c
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Page 75 and 76: 134. (a) The supplement is 180 109
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Page 79 and 80: 49. 50. 52. tan 2 tan 12 0 tan
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Page 83 and 84: 77. sin 4x 2 sin 2x cos 2x 78. 22
Page 85 and 86: 88. tan u 5 3 , < u < 8 2 sin u
Page 87: 103. 0 2 −2 Review Exercises for
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Page 93 and 94: 14. (a) cos3 cos2 (b) cos4 cos2
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C H A P T E R 5 Analytic Trigonometry

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