A-35 Answers to Selected Exercises 6.6 Exercises 1. A 3. D 5. C 7. B 9. D x y 0 –3 3 –2P 2P 4P 6P y = 3 sec x1 4 11. 0 x y 1 –1 5P 4 7P 4 3P 4 9P 4 P 4 y = sec (x + )P 4 17. y 2 –1 y = 2 + 3 sec (2x – P) x 0 5 3P 4 5P 4 P 4 23. x y 0 1 3P 2 – P 2 P 2 P y = – csc (x + )P 2 1 2 13. 0 x y 1 –1 y = csc ( x – )P 4 1 2 3P 2 5P 2 9P 2 7P 2 P 2 19. y x 1 2 0 3P 2 7P 4 3P 4 5P 2 P 2 11P 4 P 2P y = 1 – csc (x – ) 3P 4 1 2 25. 0 x y 1 –1 5P 4 9P 4 P 4 y = csc (x – )P 4 15. 0 x y 1 2 (2x + ) 1 2 3P 4 P 4 P 4 P 2 P 2 y = csc – –2 21. 27. y = sec 4x 29. y = -2 + csc x 31. y = -1 - sec x 33. true 35. true 37. none 41. 4 m 43. 63.7 m 45. The value is 1.3660254 in both cases. 47. The value is 2.4142136 in both cases. Summary Exercises on Graphing Circular Functions x y –2 –1 1 1 2 2 0 y = 2 sin Px 1. x y –3 0 1 3 –1 y = 3 sec xP 2 4. x y 5 –5 0 6P –3P 3P –6P y = –5 sin x 3 7. x y –4 4 0 P 4P 2P3P y = –4 csc x1 2 5. x y –4 4 0 4P 3 2P 3 y = 4 cos x3 2 2. x y 0 6P –10P –4P –10 10 y = 10 cos ( + )P 2 x 4 8. x y 1 –1 0 3 1 5 8 7 y = –2 + cos xP 4 1 2 3. x y 10 –10 –1 0 1 y = 3 tan ( x + P) P 2 6. x y 3 7 0 4P 5 2P 5 6P 5 5 2 2P 5 – y = 3 – 4 sin ( x + P) 9. x y 0 1 3 1 2 3 2 5 2 7 2 1 2 – y = 2 – sec[P(x – 3)] 10. 6.7 Exercises 1. 5 in. 3. 1 p oscillation per sec 5. -5 in. 7. (a) s1t2 = -4 cos 2p 3 t (b) 3.46 units (c) 1 3 oscillation per sec 9. (a) 5; 1 60 (b) 60 oscillations per sec (c) 5; 1.545; -4.045; -4.045; 1.545 (d) 0 t E –5 5 E = 5 cos 120Pt 1 120 1 40 1 60 1 30 11. (a) s1t2 = 2 sin 2t; amplitude: 2; period: p; frequency: 1 p rotation per sec (b) s1t2 = 2 sin 4t; amplitude: 2; period: p 2 ; frequency: 2 p rotation per sec 13. period: p 4 ; frequency: 4 p oscillations per sec 15. 1 p2 17. (a) 5 in. (b) 2 cycles per sec; 1 2 sec (c) after 1 4 sec (d) 4.0; After 1.3 sec, the weight is about 4 in. above the equilibrium position. 19. (a) s1t2 = -3 cos 12t (b) p 6 sec 21. (a) 1644 (b) 0.0038 sec 23. T1t2 = -0.9 cos p 12 t 25. 9 27. (a) s1t2 = 2 cos 4pt (b) s112 = 2; The weight is moving neither upward nor downward. At t = 1, the motion of the weight is changing from up to down. 29. (a) s1t2 = -3 cos 2.5pt (b) s112 = 0; upward 31. s1t2 = 0.21 cos 55pt –0.3 0 0.3 0.05 33. s1t2 = 0.14 cos 110pt –0.3 0 0.3 0.05 35. 11 in. 37. 1, 3, 5, 7, 9, 11 39. (a) –5 0 5 3 (b) y1 = 5e-0.3x (c) 0, 2 Chapter 6 Review Exercises 1. A central angle of a circle that intercepts an arc of length 2 times the radius of the circle has a measure of 2 radians. 3. Three of many possible answers are 1 + 2p, 1 + 4p, and 1 + 6p. 5. p 4 7. 35p 36 9. 40p 9 11. 225° 13. 480° 15. -110° 17. p in. 19. 12p in. 21. 35.8 cm 23. 49.06° 25. 273 m2 27. 4500 km 29. 3 4 ; 1.5 sq units 31. 23 33. - 1 2 35. 2 37. 0.8660 39. 0.9703 41. 1.9513 43. 0.3898 45. 0.5148 47. 1.1054 49. p 4 51. 7p 6 53. (a) 20p radians (b) 300p cm (c) 10p cm per sec 55. 1260p cm per sec 57. 5 in. 59. B 61. 2; 2p; none; none 63. 1 2 ; 2p 3 ; none; none 65. 2; 8p; up 1 unit; none 67. 3; 2p; none; to the left p 2 units 69. not applicable; p; none; to the right p 8 unit 71. not applicable; p 3 ; none; to the right p 9 unit 73. tangent 75. cosine 77. cotangent
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