A-33 Answers to Selected Exercises 87. 3p 32 radian per sec 89. 6 5 min 91. 8p m per sec 93. 9 5 radians per sec 95. 8 p m 97. 18p cm 99. 12 sec 101. 3p 32 radian per sec 103. p 6 radian per hr 105. p 30 radian per min 107. 30p radians per min 109. 7p 30 cm per min 111. 168p m per min 113. 1500p m per min 115. 330p mph 117. 16.6 mph 119. (a) 2p 365 radian (b) p 4380 radian per hr (c) 67,000 mph 121. (a) 3.1 cm per sec (b) 0.24 radian per sec 123. 3.73 cm 125. 523.6 radians per sec 127. 31.4 ft per sec 6.3 Exercises 1. 1; 2p 3. np 5. p 2 7. E 9. B 11. F 0 x y 2 –2 y = 2 cos x –2P –P P 2P 2 13. 0 x y –3 y = sin x 3 2 3 –2P –P P 2P 2 3 15. 0 x y –2 y = –2 sin x 2 –2P–P P 2P 2 19. x y 1 –1 y = sin (–x) –2P –P P 2P 1 21. x y 1 –2 0–1 P –4P 2P 4P y = sin x1 2 4p; 1 23. 0 x y 1 y = –cos x –2P –P P 2P 1 17. x y 1 0 y = cos x 4P 3 4P 3 8P 3 8P 3 – – 3 4 8p 3 ; 1 25. x y 1 y = sin 3x –1 0 2P 3 P 3 2P 3 – P 3 – 2p 3 ; 1 27. x y 2 0 –4P –8P 8P 4P y = 2 sin x1 4 8p; 2 29. 0 x y 1 y = –2 cos 3x 2 –2 2P 3 2P 3 – – P 3 P 3 2p 3 ; 2 31. y = cos Px 0 x y –1 –2 –1 1 2 1 2; 1 33. x y –2 –1 1 2 0 1 2 1 2 – y = –2 sin 2Px 1; 2 35. 55. (a) x y –1 –3 1 3 4 1 y = cos xP 2 1 2 1 2 0 4; 1 2 y = P sin Px y x –2 0 2 1 2 3 P –P 2; p 39. 41. y = 2 cos 2x 43. y = -3 cos 1 2 x 45. y = 3 sin 4x 47. (a) 80°F; 50°F (b) 15 (c) 35,000 yr (d) downward 15 325 385 45 L(x) = 0.022x2 + 0.55x + 316 + 3.5 sin 2px (b) maxima: x = 1 4 , 5 4 , 9 4 , . . . ; minima: x = 3 4 , 7 4 , 11 4 , . . . (c) The quadratic function provides the general increasing nature of the level, and the sine function provides the fluctuations as the years go by. 57. (a) 31°F (b) 38°F (c) 57°F (d) 58°F (e) 37°F (f) 16°F 59. 1; 240°, or 4p 3 61. No. For b 70, b≠1, the graph of y = sin bx has amplitude 1 and period 2p b , while that of y = b sin x has amplitude b and period 2p. 63. X= -0.4161468, Y= 0.90929743; X is cos 2 and Y is sin 2. 64. X= 2, Y= 0.90929743; sin 2 = 0.90929743 65. X= 2, Y= -0.4161468; cos 2 = -0.4161468 66. For an arc length T on the unit circle, X= cos T and Y= sin T. 6.4 Exercises 1. p 4 ; left 3. 4 5. 6; up 7. p 5 ; left; 5; 3; up 9. D 11. H 13. B 15. I 17. The graph of y = sin x + 1 is obtained by shifting the graph of y = sin x up 1 unit. The graph of y = sin1x + 12 is obtained by shifting the graph of y = sin x to the left 1 unit. 19. B 21. C 23. right 25. y = -1 + sin x 27. y = cos Ax - p 3 B 29. y = sin1x - p2 31. 2; 2p; none; to the left p units 33. 1 4 ; 4p; none; to the left p units 35. 3; 4; none; to the right 1 2 unit 37. 1; 2p 3 ; up 2 units; to the right p 15 unit x y –1 1 y = cos (x – ) 0 P 2 P 2 5P 2 9P 2 39. x y 1 0 –1 y = sin (x + )P 4 P 4 7P 4 3P 4 11P 4 15P 4 – 41. x y –2 2 0 y = 2 cos (x – )P 3 7P 3 4P 3 13P 3 10P 3 P 3 43. 0 x y 1 –2 –1 2 P 4 3P 4 – y = sin [2(x + )] P 4 3 2 45. y –4 y = –4 sin (2x – P) 4 0 x 3P 2 P 2 P 47. y –1 1 0 x y = cos ( x – )P 4 1 2 1 2 5P 2 9P 2 P 2 49. 37. 49. 24 hr 51. 6:00 p.m.; 0.2 ft 53. 3:18 a.m.; 2.4 ft 0 x y –1 y = –3 + 2 sin x –5 –3 2P –2P P –P 51. 0 x y 1 y = –1 – 2 cos 5x –3 2P 5 2P 5 – 53. x y 3 1 –4P 4P –3P 3P –P P y = 1 – 2 cos x1 2 55.
RkJQdWJsaXNoZXIy NjM5ODQ=