C H A P T E R 5 Analytic Trigonometry

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484 Chapter 5 Analytic Trigonometry 72. 73. tan x tan 2sin x cos cos x sin 0 1 tan x tan tan x 0 2sin x1 cos x0 0 1 tan x0 cos x cos 4 Graphically: Graph tanx 2 sinx 0 The points of intersection occur at x 4 tan x 2 sin x 0 1 sin x 2 sin x cos x sin x1 2 cos x 0 sin x 2 sin x cos x sin x 0 or cos x 1 2 Analytically: cosx 4 cosx 1 4 sin x sin 4 cos x cos 4 74. tanx cosx 0 2 Answers: 0, 0, 3.14, 0 ⇒ x 0, x 0, x 5 , 3 3 sin x sin 1 4 2 cos x 2 2 1 2 cos x 1 y1 cosx 4 cosx 4 and y2 1. and x 7 4 . 4 cos x 1 2 cos x 2 2 x 7 , 4 4 0 2 −4 0 2 −2 2
75. 76. y 1 3 1 sin 2t cos 2t 4 5 (a) a (b) Amplitude: feet 12 1 1 , b , B 2 3 4 C arctan b 3 arctan 0.6435 a 4 y 1 3 2 1 4 2 sin2t 0.6435 y 5 sin2t 0.6435 12 y1 y2 A cos 2 t x t cos T 2 t y1 y2 Acos 2 77. False. y 1 A cos 2 t y 2 A cos 2 t 2A cos 2 t x cos 2 x x sinu ± v sin u cos v ± cos u sin v 79. False. 81. 83. 84. cosx 2 x t x cos 2 sin 2 sin 2 cos x cos sin x sin 2 2 cos x0 sin x1 sin x cosn cos n cos sin n sin C arctan b a 1 n cos 0sin x 1 n cos , where n is an integer. a2 b2 sinB C a2 b2sin B C arctan a b ⇒ sin C ⇒ sin C b a2 a b2, cos C a2 b2 a a2 b2 a a2 b b2, cos C a2 b2 a2 b2 cosB C a2 b2cos B b cos B a sin B a sin B b cos B Section 5.4 Sum and Difference Formulas 485 1 B 2 1 (c) Frequency: cycle per second period t Acos 2 78. False. 2 2 x t x cos 2 sin 2 sin 2 cosu ± v cos u cos v sin u sin v 80. True. 82. b a2 sin B b2 sinx 2 sin x cos x 2 sinn sin n cos sin cos n 0cos sin 1 n 1 where n is an integer. nsin , b a2 b2 cos B a sin B b cos B a a2 b2
Page 1 and 2: 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: 69. 70. 71. sin x cos 3 cos x sin
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 and 68: 73. 75. cos sin 1 sin 5 sin 3
Page 69 and 70: 91. 93. 95. 97. 99. sin 2 5 13 2
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

C H A P T E R 5 Analytic Trigonometry

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