C H A P T E R 5 Analytic Trigonometry

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510 Chapter 5 <strong>Analytic</strong> <strong>Trigonometry</strong> 128. (a) (b) The graph appears to be that of sin 2x. (c) 130. (a) 132. (a) −2 2 −2 2 129. (a) 2 sin x2 cos2 x 2 1 2 sin x cos x 12 10 8 6 4 2 sin 2x (b) d 4 62 3 102 10 2 13 2 100 169 269 4 6 (c) Midpoint: , 2 3 10 (b) y −6 −4 2 4 6 8 10 −2 (−4, −3) (c) Midpoint: 1 16 9 (6, 10) 2 3 1 3 , 2 3 2 y 169 36 1 2 ( , ) 3 3 −2 −1 1 3 ( −1, − ) 2 1 −1 −2 d 1 2 1 3 2 3 3 2 x 2 7 1, 2 x 2 2 233 36 23 4 3 2 13 6 2 1 6 233 56 , 2 2 1 5 , 3 12 131. (a) 6 5 (−1, 4) 3 2 1 y −3 −2 −1 −1 −2 1 2 3 4 5 (b) d 1 52 4 22 62 22 40 210 (5, 2) 5 1 (c) Midpoint: , 2 2 4 3 2 1 y ( 0, ) 1 2 4 5 ( , ) 3 2 −1 1 2 x 2 2, 3 (b) 4 0 3 (c) Midpoint: 2 , 1 2 5 2 2 2 3 , 3 52 d 213 9 3 4 2 0 3 5 1 2 2 2 16 9 133. (a) Complement: 90 55 35 Supplement: 180 55 125 x 2 (b) Complement: Not possible. 162 > 90 Supplement: 180 162 18 4
134. (a) The supplement is 180 109 71. There is no complement. (b) The supplement is 180 78 102. The complement is 90 78 12. 136. (a) The supplement is The complement is 0.95 0.62. 2 (b) The supplement is There is no complement. 0.95 2.19. 2.76 0.38. 138. Let x number of gallons of 100% concentrate. 0.3055 x 1.00x 0.5055 16.50 0.30x x 27.50 0.70x 11 x 15.7 gallons Review Exercises for Chapter 5 1. 1 sec x 2. cos x 135. (a) Complement: Supplement: (b) Complement: Review Exercises for Chapter 5 511 2 2 4 18 9 18 17 18 9 20 20 Supplement: 9 11 20 20 137. Let x profit for September, then x 0.16x profit for October. 139. x x 0.16x 507,600 2.16x 507,600 x 235,000 x 0.16x 272,600 Profit for September: $235,000 Profit for October: $272,600 90 ft 90 ft Second base d Home plate 1 csc x 3. sin x 90 ft 90 ft 1 cos x sec x d 2 90 2 90 2 16,200 d 16,200 902 127 feet cos x 5. cot x sin x 4. 1 tan x cot x 6. 1 tan2 x sec2 x 7. sin x 3 4 , cos x 5 5 tan x sin x cos x 3 5 4 5 3 4 cot x 1 4 tan x 3 sec x 1 5 cos x 4 csc x 1 5 sin x 3 8. tan is in Quadrant I. 2 13 , sec 3 3 cos 1 3 313 sec 13 13 sin 1 cos2 9 1 13 csc 1 13 sin 2 cot 1 3 tan 2 sec x 4 213 13 13
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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
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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
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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 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: 125. (a) ) (b) y 4 sin x cos x 2
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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