A-34 Answers to Selected Exercises 39. y = -2 tan x 41. y = cot 3x 43. y = 1 + tan 1 2 x 45. true 47. false; tan1-x2 = -tan x for all x in the domain. 49. four 53. 0 m 55. 12.3 m 57. p 58. 5p 4 37. x y 1 0 –1 P 2 P 2 – y = 1 – 2 cot [2(x + )] P 2 61. y = –4 sin x y x 4 –4 0 P2P –2P–P 2p; 4 y = cos 2x y x P –P 1 –1 1 2 – 0 p; 1 2 11. y = –2 cos (x + ) P 4 9P 4 – y P 4 – 5P 4 – 3P 4 x –2 2 2p; 2 12. y x y = 2 + sin (2x – P) –3 1 4 P P 2 –P P 2 – p; 1 13. x y 0 1 –1 P 16 P 8 P 16 P 8 – – y = tan 4x y x 0 y = 2 tan x 2 –2 P 2 P 2 – 15. y x –2 0 2 –2P –P P 2P y = 2 tan x1 4 17. y x 0 y = cot 3x –1 1 P 3 P 6 19. x y y = cot 4x 1 2 P 4 P 8 –2 2 0 23. x y –1 1 0 y = tan (2x – P) P 2 P 4 P 3P 4 5P 4 25. y = 1 + tan x x y 1 0 P 2 3P 2 P 2 – 29. y = 1 – cot x y 1 0 x P 2 3P 2 P 2P 31. x y 1 0 –2 2 P 2 3P 2 P 2P y = –1 + cot (2x – 3P) 1 2 35. x y –2P 2P y = –2 tan x1 4 –2 2 0 21. x y –1 1 0 P 4 7P 12 P 12 – y = cot (3x + )P 4 27. y = –1 + 2 tan x x y 1 0 –1 P 2 3P 2 P 2 – P 33. 57. 59. 6.5 Exercises 1. p 3. increases 5. - p 2 7. C 9. B 11. F 13. 14. y = 2 sin x 15. y = cos 2x 10. 59. x = 5p 4 + np 60. 10.32, 02 61. 13.46, 02 62. 5x x = 0.32 + np6 (c) 12.5; 12; 4.5 (d) ƒ1x2 = 12.5 sin C p 6 1x - 4.52D + 53.5 (e) Chapter 6 Quiz [6.1] 1. 5p 4 2. -210° 3. 1.5 4. 67,500 in. 2 [6.2] 5. 22 2 6. - 1 2 7. 0 8. 2p 3 [6.3, 6.4] 9. 4; p; up 3 units; to the left p 4 unit 0 x y 1 2 –2 –P P P 2 P 2 – y = sin [2(x + )] + P 4 1 2 30 0 75 25 yes 63. (a) 30 0 75 25 y = 53.5 It represents the average annual temperature. (b) 30 0 75 25 f(x) = 12.5 sin[ (x – 4.5)] + 53.5 p 6 The function gives a good model for the given data. TI-84 Plus fixed to the nearest hundredth (f ) In the answers to Exercises 65 and 67, we give the model and one graph of the data and equation. 65. (a) See the graph in part (c). (b) y = 12.28 sin10.52x + 1.062 + 63.96 (c) 45 0 80 25 67. (a) See the graph in part (c). (b) y = 0.49 sin10.21x - 2.892 + 0.47 (c) –0.1 0 1.1 32 x y y = –2 + sin 3x –1 –2 0 1 2 2P 3 2P 3 P 3 P 3 – – x y –1 0 –5 –3 3P 2 P 2 P 2 – y = –3 + 2 sin (x + )P 2
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