A-36 Answers to Selected Exercises [6.3, 6.4] 29. (a) x y 0 –3 y = 3 sin x 3 3P 2 P 2 2 P P 79. y 1 0 –1 y = –tan x x P 2 P 2 – 81. y x 0 3 1 y = 2 + cot x 2 P 2 P 83. y –1 x 0 y = sin 2x 1 P 2 P 85. y x 1 0 y = 3 cos 2x –1 2 3 –2 –3 P P 2 87. y x 1 –1 0 P 4 9P 4 5P 4 y = cos (x – )P 4 89. y 1 x 0 –1 P 3 5P 6 13P 12 7P 12 P 12 y = sec (2x + )P 3 91. y x 0 –1 y = 1 + 2 cos 3x 2 3 1 2P 3 93. y 1 x 0 –1 y = 2 sin Px –2 2 2 1 95. 97. (a) See the graph in part (c). (b) y = 8.02 sin10.52x + 0.842 + 59.83 (c) 45 0 80 25 99. y = 1 - sin x 101. y = 2 tan 1 2 x 103. (b) d 0 50 d = 50 cot U U P 4 P 2 105. (a) 30°F (b) 60°F (c) 75°F (d) 86°F (e) 86°F (f ) 60°F 107. (a) 100 (b) 258 (c) 122 (d) 296 109. amplitude: 4; period: 2; frequency: 1 2 cycle per sec 111. The frequency is the number of cycles in one unit of time; -4 in.; 0 in.; -222 in. Chapter 6 Test [6.1] 1. 2p 3 2. - p 4 3. 0.087 4. 135° 5. -210° 6. 229° 11′ 7. (a) 4 3 (b) 15,000 cm2 8. 2 radians [6.2] 9. 22 2 10. - 23 2 11. undefined 12. -2 13. 0 14. 0 15. sin 7p 6 = - 1 2 ; cos 7p 6 = - 23 2 ; tan 7p 6 = 23 3 ; csc 7p 6 = -2 ; sec 7p 6 = - 223 3 ; cot 7p 6 = 23 16. (a) 0.9716 (b) p 3 17. (a) 2p 3 radians (b) 40p cm (c) 5p cm per sec 18. (a) 75 ft (b) p 45 radian per sec 23. 1 y x P 2 P –P P 2 – y = sin (2x + P) –1 0 24. y = 2 + cos x –P –2P P 2P 3 x y 25. y x –1 –2 –3 2 3 y = –1 + 2 sin (x + P) 0 –2P –P P 2P [6.5] 26. y x 0 1 –1 x = P x = –P –P P y = tan (x – )P 2 27. x y –2 0 3P 2 P 2 P 2 P – y = –2 – cot (x – )P 2 [6.6] 28. x y 0 –1 1 2 –2 3P 2 P 2 P 2P y = –csc 2x [6.3 – 6.6] 19. (a) y = sec x (b) y = sin x (c) y = cos x (d) y = tan x (e) y = csc x (f ) y = cot x 20. (a) y = 1 + cos 1 2 x (b) y = - 1 2 cot x [6.3, 6.5, 6.6] 21. (a) 1-∞, ∞2 (b) 3-1, 14 (c) p 2 (d) 1-∞, -14 ´31, ∞2 [6.4] 22. (a) p (b) 6 (c) 3-3, 94 (d) 10, -32 (e) to the left p 4 unit 40 0 90 25 f(x) = 16.5 sin[ (x – 4)] + 68.5 p 6 (b) 16.5; 12; to the right 4 units; up 68.5 units (c) 54°F (d) 52°F in January; 85°F in July (e) 68.5°F; This is the vertical translation. [6.7] 30. (a) 4 in. (b) after 1 8 sec (c) 4 cycles per sec; 1 4 sec Chapter 7Trigonometric Identities and Equations 7.1 Exercises 1. B 3. E 5. A 7. -0.65 9. -0.75 11. 27 4 13. - 5 226 26 15. - 225 5 17. - 215 5 19. - 2105 11 21. - 4 9 23. sin u is the reciprocal of csc u and therefore has the same sign. 25. ƒ1-x2 = -sin x -x = sin x x = ƒ1x2; even 27. ƒ1x2 = sec x; even 29. ƒ1x2 = cot x; odd 31. cos u = - 25 3 ; tan u = - 225 5 ; cot u = - 25 2 ; sec u = - 325 5 ; csc u = 3 2 33. sin u = - 217 17 ; cos u = 4217 17 ; cot u = -4; sec u = 217 4 ; csc u = - 217 35. sin u = 3 5 ; cos u = 4 5 ; tan u = 3 4 ; sec u = 5 4 ; csc u = 5 3
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