Review Exercises AN51 Review Exercises (page 466) 1. 3 4 π 2. 10 π 3. 135° 4. 450 − ° 5. 1 2 6. 3 2 2 4 3 3 − 7. 3 2 2 3 − − 8. 3 9. 0 10. 0 11. 1 12. 1 13. 1 14. 1− 15. 1 16. cos 3 5 ; tan 4 3 ; csc 5 4 ; sec 5 3 ; cot 3 4 θ θ θ θ θ = = = = = 17. sin 12 13 ; cos 5 13 ; csc 13 12 ; sec 13 5 ; cot 5 12 θ θ θ θ θ = − = − = − = − = 18. sin 3 5 ; cos 4 5 ; tan 3 4 ; csc 5 3 ; cot 4 3 θ θ θ θ θ = = − = − = = − 19. cos 5 13 ; tan 12 5 ; csc 13 12 ; sec 13 5 ; cot 5 12 θ θ θ θ θ = − = − = = − = − 20. cos 12 13 ; tan 5 12 ; csc 13 5 ; sec 13 12 ; cot 12 5 θ θ θ θ θ = = − = − = = − 21. sin 10 10 ; cos 3 10 10 ; csc 10; sec 10 3 ; cot 3 θ θ θ θ θ = − = − = − = − = 22. sin 2 2 3 ; cos 1 3 ; tan 2 2; csc 3 2 4 ; cot 2 4 θ θ θ θ θ = − = = − = − = − 23. sin 5 5 ; cos 2 5 5 ; tan 1 2 ; csc 5; sec 5 2 θ θ θ θ θ = = − = − = = − 24. y 2.5 x P 3P 8 , 22 P 8 , 2 Domain: , ( ) −∞ ∞ Range: 2, 2 [ ] − 25. P 2 , 3 (P, 23) y 5 x P Domain: , ( ) −∞∞ Range: 3, 3 [ ] − 26. P 2 y 5 x x x k k Domain: 2 , is an odd integer π { } ≠ Range: , ( ) −∞∞ 27. P 6 2 x 5 P 2 8 y x x x k k Domain: 6 3 , is an integer π π { } ≠ + ⋅ Range: , ( ) −∞∞ 28. 3P 4 y 5 x P x 5 x x k k Domain: 4 , is an integer π π { } ≠ − + Range: , ( ) −∞∞ 29. y x 23 5P 4 P 2 , 24 x x k k Domain: 4 , is an odd integer π { } ≠ y y y Range: 4 or 4 { } ≤− ≥ 30. y x 4P 5 x x k k Domain: 4 , is an integer π π { } ≠ − + y y y Range: 1 or 1 { } ≤− ≥ 31. y x 27 5 Domain: , ( ) −∞∞ Range: 6, 2 [ ] − 32. y 25 x 5P x x k k Domain: 3 4 3 , is an integer π π { } ≠ + ⋅ Range: , ( ) −∞∞ 33. Amplitude 1; Period π = = 34. Amplitude 2; Period 2 3 = = 35. Amplitude 4 = Period 2 3 π = Phase shift 0 = P 2 , 24 P 6 , 4 y x 5 P 36. Amplitude 1 = Period 4π = Phase shift π = − y x 5P 2.5 37. Amplitude 1 2 = Period 4 3 π = Phase shift 2 3 π = y x 2P 1.25 38. Amplitude 2 3 = Period 2 = Phase shift 6 π = y x 12 P 2 3 39. y x 5cos 4 = 40. y x 7sin 4 π( ) = − 41. 0.38 42. 1.02 43. Sine, cosine, cosecant, and secant: negative; tangent and cotangent: positive 44. IV 45. sin 2 2 3 ; cos 1 3 ; tan 2 2; csc 3 2 4 ; sec 3; cot 2 4 θ θ θ θ θ θ = = − = − = = − = − 46. t t t sin 5 29 29 , cos 2 29 29 , tan 5 2 = = − = − 47. Domain: x x odd multiple of 2 ; π { } ≠ range: y y y 1 or 1 { } ≤− ≥ 48. (a) 32.34° (b) 63 10 48 ° ′ ″ 49. 3 1.05 ft; 3 1.05 ft2 π π ≈ ≈ 50. 8 25.13 in.; 16 3 16.76 in. π π ≈ ≈ 51. Approximately 114.59 revolutions/hr 52. π = 0.1 revolution sec 5 radian sec
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