A-45 Answers to Selected Exercises 33. x y 2 1 0 x = 2 + sin t y = 1 + cos t for t in [0, 2P] 1x - 222 + 1y - 122 = 1 Answers may vary for Exercises 35, 37, and 39. 35. x = t, y = 1t + 322 - 1, for t in 1-∞, ∞2; x = t - 3, y = t2 - 1, for t in 1-∞, ∞2 37. x = t, y = t2 - 2t + 3, for t in 1-∞, ∞2; x = t + 1, y = t2 + 2, for t in 1-∞, ∞2 39. x = t, y = t2 - 2t + 1, for t in 1-∞, ∞2; x = t + 1, y = t2, for t in 1-∞, ∞2 41. y x x = 2t – 2 sin t y = 2 – 2 cos t for t in [0, 4P] 0 4 4P 2P 6P 8P 43. y x 0 1 P 2P x = 0.5(t – sin t) y = 0.5(1 – cos t) for t in [0, 4P] P 2 3P 2 45. –4 –6 4 x = 3 sin 4t, y = 3 cos 3t, for t in [0, 6.5] 6 47. (a) x = 24t, y = -16t2 + 2423 t (b) y = - 1 36 x 2 + 23 x (c) 2.6 sec; 62 ft 49. (a) x = 188 cos 20°2t, y = 2 - 16t2 + 188 sin 20°2t (b) y = 2 - x 2 484 cos2 20° + 1tan 20°2x (c) 1.9 sec; 161 ft 51. (a) y = - 1 256 x 2 + 23 x + 8; parabolic path (b) 7 sec; 448 ft 53. (a) x = 32t, y = 3223 t - 16t2 + 3 (b) 112.6 ft (c) 51 ft maximum height; The ball had traveled horizontally 55.4 ft. (d) yes 55. Many answers are possible; for example, y = a1t - h22 + k, x = t and y = at2 + k, x = t + h. 57. Many answers are possible; for example, x = a sin t, y = b cos t and x = t, y2 = b2 Q1 - t 2 a2R . Chapter 8 Review Exercises 1. 63.7 m 3. 41.7° 5. 54° 20′ or 125° 40′ 7. If one side and two angles are given, the third angle can be determined using the angle sum formula, and then the ASA axiom can be applied. This is not the ambiguous case. 9. (a) b = 5, b Ú 10 (b) 5 6b 610 (c) b 65 11. 19.87°, or 19° 52′ 13. 55.5 m 15. 19 cm 17. B = 17.3°, C = 137.5°, c = 11.0 yd 19. c = 18.7 cm, A = 91° 40′, B = 45° 50′ x y –3 0 –2 3 2 x = 3 sin t y = 2 cos t for t in [0, 2P] x2 9 + y2 4 = 1 x y –3 0 –3 3 3 x = 3 cos t y = 3 sin t for t in [0, 2P] x2 + y2 = 9 29. 31. 21. 153,600 m2 23. 0.234 km2 25. 58.6 ft 27. 13 m 29. 53.2 ft 31. 115 km 33. 25 sq units 35. a –b a – b y x 0 3 – 3i√3 –5 3 5i y x 0 61. 63. 65. 2221cos 135° + i sin 135°2 67. -22 - i22 69. 221cos 315° + i sin 315°2 71. 41cos 270° + i sin 270°2 73. It is the line y = -x. 75. 26 21cos 105° +i sin 105°2, 26 21cos 225° + i sin 225°2, 26 21cos 345° + i sin 345°2 77. none 79. 521cos 45° + i sin 45°2, 21cos 135° + i sin 135°2, 21cos 225° + i sin 225°2, 21cos 315° + i sin 315°26 81. 5cos 135° + i sin 135°, cos 315° + i sin 315°6 83. 12, 120°2 85. circle 87. eight-leaved rose 1808 08 908 2708 2 r = 2 sin 4U 1 1808 08 908 2708 4 r = 4 cos U 89. y2 = -6 Ax - 3 2B , or y 2 + 6x - 9 = 0 91. x2 + y2 = 4 93. r = tan u sec u, or r = tan u cos u 95. r = 2 sec u, or r = 2 cos u 97. r = 4 cos u + 2 sin u 99. x y x = t + cos t y = sin t for t in [0, 2P] 1 0 (P – 1, 0) (2P + 1, 0) ( , –1) ( , 1) 3P 2 P 2 101. y = 2x2 + 1, for x in 30, ∞2 103. y = 331 + x 2 25 , for x in 1-∞, ∞2 105. y2 = - 1 2 1x - 12, or 2y2 + x - 1 = 0, for x in 3-1, 14 y = 3.2 - 16t2 + 1118 sin 27°2t (b) y = 3.2 - 4x 2 3481 cos2 27° + 1tan 27°2x (c) 3.4 sec; 358 ft Chapter 8Test [8.1] 1. 137.5° [8.2] 2. 179 km 3. 49.0° 4. 168 sq units [8.1] 5. 18 sq units 6. (a) b 710 (b) none (c) b … 10 [8.1– 8.2] 7. a = 40 m, B = 41°, C = 79° 8. B1 = 58° 30′, A1 = 83° 00′, a1 = 1250 in.; B2 = 121° 30′, A2 = 20° 00′, a2 = 431 in. 37. 207 lb 39. -869; 418 41. 15; 126.9° 43. (a) i (b) 4i - 2j (c) 11i - 7j 45. 90°; orthogonal 47. 29 lb 49. bearing: 306°; ground speed: 524 mph 51. 34 lb 53. -30i 55. - 1 8 + 23 8 i 57. 8i 59. - 1 2 - 23 2 i 107. (a) x = 1118 cos 27°2t,
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