C H A P T E R 5 Analytic Trigonometry

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504 Chapter 5 <strong>Analytic</strong> <strong>Trigonometry</strong> 87. 88. 89. 6x 2x 6x 2x 2 sin 2 cos 2 0 sin 4x 0 or cos 2x 0 4x n or cos 2x n 2 x n 4 sin 6x sin 2x 0 2 sin 4x cos 2x 0 n or cos 2x 4 2 In the interval we have x 0, 3 5 3 7 , , , , , , 4 2 4 4 2 4 . 0, 2 2 sin 4x sin2x 0 sin 4x 0 0 2 −2 cos 2x cos 6x 0 2 sin 4x sin 2x 0 4x n x n 4 hx cos 2x cos 6x x 0, 3 5 3 7 , , , , , , 4 2 4 4 2 4 cos 2x 1 sin 3x sin x cos 2x 1 2 cos 2x sin x 2 sin x 1 sin x 1 2 x 5 , 6 6 2 or 0 2 −2 sin 2x 0 2x n x n 2 2 x 0, 3 , , 2 2 cos 2x 1 0 90. sin 3x sin x 0 1 −1 0 2 −2 sin 3x sin xsin 3x sin x 0 2 sin 2x cos x2 cos 2x sin x 0 sin 2x 0 ⇒ x 0, 3 , , 2 2 or cos x 0 ⇒ x 3 , 2 2 or cos 2x 0 ⇒ x 3 5 7 , , , 4 4 4 4 or sin x 0 ⇒ x 0, 2 2 sin 2 3x sin 2 x 0 fx sin 2 3x sin 2 x
91. 93. 95. 97. 99. sin 2 5 13 2 25 169 sin 2 1 cos 2 1 12 13 2 sin cos 5 13 4 4 5 13 sin cos cos 2 csc 2 1 sin 2 5 13 4 4 5 13 1 2 sin cos 1 sin 1 2 cos csc 2 cos 1 144 25 169 169 sin 2 cos 2 2 sin 2 2 cos22 cos 4 sin x cos x 2 sin 2 x 2 sin x cos x cos 2 x Section 5.5 Multiple-Angle and Product-to-Sum Formulas 505 5 3 β α 4 sin 2 x cos 2 x 2 sin x cos x 1 sin 2x 101. 1 cos 10y 1 cos2 5y sin2 5y 1 cos 2 5y 1 cos 2 5y 2 cos 2 5y 13 12 Figure for Exercises 91–94 92. 94. 96. 98. 100. 5 cos2 cos 2 12 13 2 144 169 cos 2 1 sin 2 1 5 13 2 1 25 144 169 169 cos sin 12 13 3 36 5 65 cos sin sin 2 sec 2 1 cos 2 12 13 3 36 5 65 cos 2 1 cos 2 sin 2 1 cos 2 1 sin2 cos 2 sec2 1 tan 2 sec 2 1 sec 2 1 sec2 2 sec 2 cos 4 x sin 4 x cos 2 x sin 2 xcos 2 x sin 2 x cos 2x1 cos 2x sin 1 3 cos 3 22sin3 cos3 1 2 sin 2 3
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CHAPTER 5 Analytic Trigonometry Sec
Page 3 and 4:
1. sin x 3 , cos x 1 2 2 tan x si
Page 5 and 6:
19. 22. 24. 26. sinx sin x tan x 2
Page 7 and 8:
53. sin 4 x cos 4 x sin 2 x cos
Page 9 and 10:
74. 75. 76. y 1 sec x csc x tan x
Page 11 and 12:
88. 90. 92. 94. 96. cos 1 sin 2
Page 13 and 14:
Section 5.1 Using Fundamental Ident
Page 15 and 16:
5. cos 2 sin 2 1 sin 2 sin 2
Page 17 and 18: 28. 30. 32. 33. 1 sin y1 siny 1
Page 19 and 20: 43. (a) (b) (c) 45. (a) 47. (b) (c)
Page 21 and 22: 61. 63. 65. 67. 2 3i 26 2 3i 2
Page 23 and 24: 5. 7. 2 sin2 x sin x 1 0 6. csc4
Page 25 and 26: 24. 26. 28. 30. 2 sin 2 x 2 cos x
Page 27 and 28: 40. 42. 44. sin x 2 3 2 x 2 4 2n
Page 29 and 30: 56. 3 tan 2 x 4 tan x 4 0 tan x
Page 31 and 32: 64. (a) f x 2 sin x cos 2x max: 0
Page 33 and 34: 75. —CONTINUED— 76. (a) (b) The
Page 35 and 36: 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
Page 43 and 44: 37. 39. 41. sinu v sin u cos v c
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
Page 49 and 50: 75. 76. y 1 3 1 sin 2t cos 2t 4 5
Page 51 and 52: 93. y1= m1x + b1 α y θ δ β y2=
Page 53 and 54: 97. 99. f x 5x 3 98. f 1 x y 5x
Page 55 and 56: Section 5.5 Multiple-Angle and Prod
Page 57 and 58: 15. 17. tan 2x cot x 0 16. 2 tan
Page 59 and 60: 26. 27. 28. 29. cot u 4, 3 2 < u <
Page 61 and 62: 33. 1 sin 1 cos 2x1 cos 2x1 cos
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
Page 67: 73. 75. cos sin 1 sin 5 sin 3
Page 71 and 72: 111. 112. 114. −2 2 −3 cos 3 c
Page 73 and 74: 125. (a) ) (b) y 4 sin x cos x 2
Page 75 and 76: 134. (a) The supplement is 180 109
Page 77 and 78: 24. 26. sin12 x cos x 1 sin x cos
Page 79 and 80: 49. 50. 52. tan 2 tan 12 0 tan
Page 81 and 82: 61. 7 5 4 13 3 4 12 13 1 57 3
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 and 88: 103. 0 2 −2 Review Exercises for
Page 89 and 90: 1. —CONTINUED— 2. 4. (b) cos si
Page 91 and 92: 7. The hypotenuse of the larger rig
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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