A-39 Answers to Selected Exercises Chapter 7 Quiz [7.5] 1. 1 0 (1, 0) –1 (–1, P) P P 2 (0, ) x y y = cos–1 x 3-1, 14; 30, p4 (d) 0 –2 2 0.03 sin[2p(220)t] + 1 2 For x = t, P(t) = sin[2p(110)t] + sin[2p(330)t] + 1 3 sin[2p(440)t] 1 4 2. (a) - p 4 (b) p 3 (c) 5p 6 3. (a) 22.568922° (b) 137.431085° 4. (a) 5 241 41 (b) 23 2 [7.6] 5. 560°, 120°6 6. 560°, 180°, 300°6 7. (a) 0 sec (b) 0.20 sec 8. 50.6089, 1.3424, 3.7505, 4.48406 9. Ep 6 , 2p 3 , 7p 6 , 5p 3 F 10. E5p 3 + 4np, 7p 3 + 4np, where n is any integerF 7.7 Exercises 1. C 3. C 5. A 7. x = arccos y 5 9. x = 1 2 arctan y 3 11. x = 4 arccos y 6 13. x = 1 5 arccos A - y 2B 15. x = arcsin1y + 22 17. x = arcsin y + 4 2 19. x = 1 3 arccot 2y 21. x = -3 + arccos y 23. x = 1 2 sec-1 Qy - 22 3 R 25. U - 22 2 V 27. E -2 22F 29. ∅ 31. E4 5F 33. E 5 7F 35. E 3 5F 37. 5p - 36 39. 506 41. E1 2F 43. ∅ 45. E - 1 2F 47. 506 49. E23 3 , 23 F 51. 54.46226 113. (a) when x = 7 (during July) (b) when x = 1.8 (during January) and when x = 12.2 (during December) 115. 0.001 sec 117. 0.004 sec 111. (a) 0 –1 1 0.03 For x = t, P(t) = sin[2p(220)t] + 1 2 sin[2p(330)t] + 1 3 sin[2p(440)t] 1 4 (b) 0.0007576, 0.009847, 0.01894, 0.02803 (c) 110 Hz 53. (a) A ≈0.00506, f≈0.484; P = 0.00506 sin1440pt + 0.4842 (b) 0 –0.006 0.006 0.01 For x = t, P(t) = 0.00506 sin(440pt + 0.484) P1(t) + P2(t) = 0.0012 sin(440pt + 0.052) + 0.004 sin(440pt + 0.61) The two graphs are the same. 55. (a) tan a = x z ; tan b = x + y z (b) x tan a = x + y tan b (c) a = arctan A x tan b x + y B (d) b = arctan A1x + y2 tan a x B 57. (a) t = 1 2pƒ arcsin E Emax (b) 0.00068 sec 59. (a) t = 3 4p arcsin 3y (b) 0.27 sec Chapter 7 Review Exercises 1. B 3. C 5. D In Exercises 7–11, there may be more than one possible answer. 7. 1 9. sec2 u 11. -cot u 13. sin x = - 4 5 ; tan x = - 4 3 ; cot1-x2 = 3 4 15. sin 165° = 26 - 22 4 ; cos 165° = - 26 - 22 4 ; tan 165° = -2 + 23 ; csc 165° = 26 + 22 ; sec 165° = -26 + 22 ; cot 165° = -2 - 23 17. I 19. H 21. G 23. J 25. F 27. 117 125 ; 4 5 ; - 117 44 ; II 29. 2 + 327 10 ; 223 + 221 10 ; -2523 - 8221 9 ; II 31. 4 - 9211 50 ; 12211 - 3 50 ; 211 - 16 21 ; IV 33. sin u = 214 4 ; cos u = 22 4 35. sin 2x = 3 5 ; cos 2x = - 4 5 37. 1 2 39. 25 - 1 2 41. 0.5 43. sin 2x + sin x cos x - cos 2x = cot x 2 45. sin x 1 - cos x = cot x 2 47. 21sin x - sin3 x2 cos x = sin 2x 71. y x 1 –1 (0, 0) y = sin–1 x P 2 P 2 – P 2 (–1, – ) P 2 (1, ) (–1, P) x y y = cos–1 x (1, 0) –1 0 1 P 2 (0, ) P y x P 4 (1, ) P 2 1 2 (0, 0) –2 P 2 – P 4 (–1, – ) y = tan–1 x 3-1, 14; C - p 2 , p 2 D 3-1, 14; 30, p4 1-∞, ∞2; A - p 2 , p 2 B 73. false; arcsin A - 1 2B = - p 6 , not 11p 6 . 75. p 4 77. - p 3 79. 3p 4 81. 2p 3 83. 3p 4 85. -60° 87. 60.67924514° 89. 36.4895081° 91. 73.26220613° 93. -1 95. 3p 4 97. p 4 99. 27 4 101. 23 2 103. 294 + 12526 92 105. 1 u
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