AN50 Answers: Chapter 6 11. Amplitude 4 = Period 2 = Phase shift 2 π = − 2 P 1 2 2 , 29 2 2 P 2 , 25 2 P 3 2 2 , 29 2 P 1 2 2 , 21 2 P 1 2 , 25 2 P 2 2 , 25 y 1 x 2 13. Amplitude 3 = Period 2 = Phase shift 2 π = 2 P , 8 2 P 21 1 , 2 2 P 1 1 , 2 2 P 2 1 , 8 y 9 x 3 15. Amplitude 3 = Period π = Phase shift 4 π = P 2 , 3 P 4 , 0 3P 4 , 0 2 3P 4 , 0 P 4 , 0 2 P 2 , 3 2 (2P, 23) (P, 23) (0, 23) y 5 x P 17. P 4 P 4 3P 16 , 2 5P 16 , 22 3P 16 , 22 5P 16 , 0 , 0 2 2 2 , 2 y 5 x (0, 0) P 2 19. 5P 8 , 3 2 3P 8 , 3 7P 8 , 23 P 8 , 23 x 5 P 8 5P 8 3P 8 7P 8 y 5 x P 2 x 52 x 5 x 52 21. Amplitude 2 = Period 2 π = Phase shift 4 π = − 3P 8 , 1 P 4 , 21 2 P 8 P 4 , 21 P 2 , 3 P 8 , 1 P 2 P 22 6 x y , 1 (0, 3) 2 25 23. ( ) = ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ y x 2 sin 2 1 2 or ( ) = − y x 2 sin 2 1 25. ( ) = ⎡ + ⎣ ⎢ ⎤ ⎦ ⎥ y x 3sin 2 3 1 3 or ( ) = + y x 3sin 2 3 2 9 27. Period 1 15 sec = Amplitude 120 amp = Phase shift 1 90 sec = 2 15 I 120 t 29. (a) H 10 5 10 20 30 x (b) y x 8.5 sin 2 5 11 4 24.5 π( ) = ⎡ − ⎢ ⎣ ⎤ ⎦ ⎥ + or y x 8.5 sin 2 5 11 10 24.5 π π ( ) = − + (c) H 10 5 10 20 30 x (d) y x 9.52 sin 1.229 2.976 24.230 ( ) = + + (e) 0 11 10 40 31. (a) y 20 5 10 50 80 x (b) y x 23.65 sin 6 4 51.75 π ( ) = ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ + or y x 23.65 sin 6 2 3 51.75 π π ( ) = − + 0 14 86 13 (d) y x 24.25 sin 0.493 1.927 51.61 ( ) = − + (e) (c) y 20 5 10 50 80 x 33. (a) 1:35 pm (b) y x y x 2.94 sin 24 149 1.934 2.79 or 2.94 sin 24 149 0.979 2.79 π π ( ) = ⎡ + ⎣ ⎢ ⎤ ⎦ ⎥ + = ⎡ + ⎣ ⎢ ⎤ ⎦ ⎥ + (c) 2.33 ft 35. (a) y x 1.615 sin 2 365 1.39 12.135 π ( ) = − + (b) 12.42 hr (c) x 10 150 280 420 y 20 (d) The actual hours of sunlight on April 1, 2022 were 12.43 hours. This is very close to the predicted amount of 12.42 hours. 37. (a) y x 6.96 sin 2 365 1.39 12.41 π ( ) = − + (b) 13.63 hr (c) x 10 150 280 420 y 20 (d) The actual hours of sunlight on April 1, 2022 were 13.37 hours. This is close to the predicted amount of 13.63 hours. 39. y t y t 51 sin 5 9 0.9 55 or 51 sin 5 9 2 55 π π π ( ) ( ) = ⎡ + ⎣ ⎢ ⎤ ⎦ ⎥ + = + + 42. f x x2 9 4 1( ) = − − 43. 7 3{ } 44. x xy y 64 240 225 2 2 + + 45. 2 13 46. 3 8 , 11 2 { } 47. y u u y u u 4 or 4 3 2 1 2 ( ) = − = − 48. a a x 1 2 2 − 49. 8 ft 19 ft × 50. x 3 = − 51. x y 3 2 log 5 log 2 2 + +
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