C H A P T E R 5 Analytic Trigonometry

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456 Chapter 5 <strong>Analytic</strong> <strong>Trigonometry</strong> 49. 51. 53. 54. 55. 56. (a) sin 2 x sin 4 x cos x sin 2 x1 sin 2 x cos x 50. sin 2 x cos 2 x cos x sin 2 x cos 3 x sin 2 25 sin 2 65 sin 2 25 cos 2 90 65 52. sin 2 25 cos 2 25 1 cos 2 20 cos 2 52 cos 2 38 cos 2 70 cos 2 20 cos 2 52 sin 2 90 38 sin 2 90 70 cos 2 20 cos 2 52 sin 2 52 sin 2 20 cos 2 20 sin 2 20 cos 2 52 sin 2 52 1 1 sin 2 12 sin 2 40 sin 2 50 sin 2 78 sin 2 12 sin 2 78 sin 2 40 sin 2 50 cos x csc x cot x cos x 1 sin x (b) h sin90 sin 10 1 cos x1 sin2 x cos x1 csc 2 x cos xcsc 2 x 1 cos x cot 2 x 20 cos x sin x h cos h cot sin 30 40 2 cos 2 90 12 sin 2 78 cos 2 90 40 sin 2 50 cos 2 78 sin 2 78 cos 2 50 sin 2 50 1 1 2 s 28.36 13.74 8.66 5.96 4.20 2.89 1.82 0.88 0 50 57. False. For the equation to be an identity, it must be true for all values of in the domain. 60 70 80 sin 4 x cos 4 x sin 2 x sin 2 x cos 4 x 1 cos 2 x1 cos 2 x cos 4 x 1 2 cos 2 x cos 4 x cos 4 x 1 2 cos 2 x 2 cos 4 x cos 2 55 cos 2 35 cos 2 55 sin 2 90 35 90 cos 2 55 sin 2 55 1 58. True. An identity is an equation that is true for all real values in the domain of the variable. 59. Since then if lies in Quadrant III or IV. One such angle is 7 4 . sin 1 cos2 sin ±1 cos 2 sin ; 2 1 cos2 , 60. True identity: tan sec is not true for 2 < < 32 < < 2. Thus, the equation is not true for or 2 tan ±sec 1 2 tan sec 1 2 1 34. (c) Greatest: 10, Least: 90 (d) Noon
61. 63. 65. 67. 2 3i 26 2 3i 26i 62. 2 3 26 i 16 1 4 4i1 2i 64. 4i 8i 2 4i 8 8 4i x 2 6x 12 0 66. a 1, b 6, c 12 x 6 ± 62 4112 21 6 ± 36 48 2 6 ± 84 2 6 ± 221 2 3 ± 21 3x 2 6x 12 0 68. 3x 2 2x 4 0 x 2 2x 4 0 a 1, b 2, c 4 x 2 ± 22 414 21 2 ± 4 16 2 2 ± 20 2 2 ± 25 2 1 ± 5 Section 5.2 Verifying Trigonometric Identities 457 2 5i 2 2 5i2 5i 4 20i 25i 2 4 20i 25 21 20i 3 2i 3 3 2i3 2i3 2i x 4 ± 47 16 9 12i 4i 2 3 2i 5 12i3 2i 15 10i 36i 24i 2 9 46i x 2 5x 7 0 a 1, b 5, c 7 x 5 ± 52 417 21 x 5 ± 53 2 8x 2 4x 3 0 a 8, b 4, c 3 x 4 ± 42 483 28 4 ± 112 16 x 1 1 ± 7 4
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: 43. (a) (b) (c) 45. (a) 47. (b) (c)
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 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
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