A-40 Answers to Selected Exercises 107. 50.4636, 3.60526 109. Ep 4 , 3p 4 , 5p 4 , 7p 4 F 111. Ep 8 , 3p 8 , 5p 8 , 7p 8 , 9p 8 , 11p 8 , 13p 8 , 15p 8 F 113. E p 3 + 2np, p + 2np, 5p 3 + 2np, where n is any integerF 115. 5270°6 117. 545°, 90°, 225°, 270°6 119. 570.5°, 180°, 289.5°6 121. 5300° + 720°n, 420° + 720°n, where n is any integer6 123. 5180° + 360°n, where n is any integer6 125. ∅ 127. E - 1 2F 129. x = arcsin 2y 131. x = A1 3 arctan 2yB - 2 3 133. (b) 0 –0.5 1 20 ( ) 15 x ( ) 5 x y1 = tan –1 – tan–1 8.6602534 ft; There may be a discrepancy in the final digits. 135. No light will emerge from the water. Chapter 7Test [7.1] 1. sin u = - 7 25 ; tan u = - 7 24 ; cot u = - 24 7 ; sec u = 25 24 ; csc u = - 25 7 2. cos u 3. -1 [7.3] 4. 26 - 22 4 5. (a) -sin u (b) tan x [7.4] 6. - 32 - 22 2 [7.3] 7. (a) 33 65 (b) - 56 65 (c) 63 16 (d) II [7.4] 8. (a) - 7 25 (b) - 24 25 (c) 24 7 (d) 25 5 (e) 2 [7.3] 13. (a) V = 163 cos A p 2 - vtB (b) 163 volts; 1 240 sec [7.5] 14. y x 1 –1 (0, 0) y = sin–1 x P 2 P 2 – P 2 (–1, – ) P 2 (1, ) 3-1, 14; C - p 2 , p 2 D 15. (a) 2p 3 (b) - p 3 (c) 0 (d) 2p 3 16. (a) 30° (b) -45° (c) 135° (d) -60° 17. (a) 43.97° (b) 22.72° (c) 125.47° 18. (a) 25 3 (b) 422 9 19. u 21 - u2 1 - u2 [7.6] 20. 530°, 330°6 21. 590°, 270°6 22. 518.4°, 135°, 198.4°, 315°6 23. E0, 2p 3 , 4p 3 F 24. E p 12 , 7p 12 , 3p 4 , 5p 4 , 17p 12 , 23p 12 F 25. 50.3649, 1.2059, 3.5065, 4.34756 26. 590° + 180°n, where n is any integer6 27. E2p 3 + 4np, 4p 3 + 4np, where n is any integerF [7.7] 28. (a) x = 1 3 arccos y (b) x = arccot y - 4 3 29. (a) E 4 5F (b) E 23 3 F [7.6] 30. P first reaches its maximum at approximately 2.5 * 10-4. The maximum is approximately 0.003166. Chapter 8 Applications ofTrigonometry Note to student: Although most of the measures resulting from solving triangles in this chapter are approximations, for convenience we use =rather than ?in the answers. 8.1 Exercises 1. The law of sines may be used. 3. There is not sufficient information to use the law of sines. 5. A 7. (a) 4 6L 65 (b) L = 4 or L 75 (c) L 64 9. 1 11. 0 13. 23 15. C = 95°, b = 13 m, a = 11 m 17. B = 37.3°, a = 38.5 ft, b = 51.0 ft 19. C = 57.36°, b = 11.13 ft, c = 11.55 ft 21. B = 18.5°, a = 239 yd, c = 230 yd 23. A = 56° 00′, AB = 361 ft, BC = 308 ft 25. B = 110.0°, a = 27.01 m, c = 21.36 m 27. A = 34.72°, a = 3326 ft, c = 5704 ft 29. C = 97° 34′, b = 283.2 m, c = 415.2 m 31. 45° 33. B1 = 49.1°, C1 = 101.2°, B2 = 130.9°, C2 = 19.4° 35. B = 26° 30′, A = 112° 10′ 37. No such triangle exists. 39. B = 27.19°, C = 10.68° 41. B = 20.6°, C = 116.9°, c = 20.6 ft 43. No such triangle exists. 45. B1 = 49° 20′, C1 = 92° 00′, c1 = 15.5 m; B2 =130° 40′, C2 = 10° 40′, c2 = 2.88 m 47. B = 37.77°, C = 45.43°, c = 4.174 ft 49. A1 = 53.23°, C1 = 87.09°, c1 = 37.16 m; A2 = 126.77°, C2 = 13.55°, c2 = 8.719 m 51. 1; 90°; a right triangle 53. Because A is obtuse, it is the largest angle. Thus side a should be the longest side, but it is not. Therefore, no such triangle exists. 55. 118 m 57. 17.8 km 59. first location: 5.1 mi; second location: 7.2 mi 61. 0.49 mi 63. 111° 65. 664 m 67. 218 ft 69. The distance is 419,000 km, which compares favorably to the actual value. 71. 23 2 sq unit 73. 22 2 sq unit 75. 46.4 m2 77. 356 cm2 79. 722.9 in.2 81. 65.94 cm2 83. 100 m2 85. a = sin A, b = sin B, c = sin C 87. x = d sin a sin b sin1b - a2 90. = 1.12257R2 91. (a) 8.77 in.2 (b) 5.32 in.2 92. red 8.2 Exercises 1. (a) SAS (b) law of cosines 3. (a) SSA (b) law of sines 5. (a) ASA (b) law of sines 7. (a) SSS (b) law of cosines 9. 5 11. 120° 13. a = 7.0, B = 37.6°, C = 21.4° 15. A = 73.7°, B = 53.1°, C = 53.1° (The angles do not sum to 180° due to rounding.) 17. b = 88.2, A = 56.7°, C = 68.3° 19. a = 2.60 yd, B = 45.1°, C = 93.5° 21. c = 6.46 m, A = 53.1°, B = 81.3° 23. A = 82°, B = 37°, C = 61° 25. C = 102° 10′, B = 35° 50′, A = 42° 00′ 27. C = 84° 30′, B = 44° 40′, A = 50° 50′ 29. a = 156 cm, B = 64° 50′, C = 34° 30′
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