Cumulative Review AN65 Review Exercises (page 593) 1. sin 4 5 ; cos 3 5 ; tan 4 3 ; cot 3 4 ; sec 5 3 ; csc 5 4 θ θ θ θ θ θ = = = = = = 2. sin 3 2 ; cos 1 2 ; tan 3; cot 3 3 ; sec 2; csc 2 3 3 θ θ θ θ θ θ = = = = = = 3. 0 4. 1 5. 1 6. A b a 70 , 3.42, 9.40 = ° ≈ ≈ 7. a A B 4.58, 66.4 , 23.6 ≈ ≈ ° ≈ ° 8. C b c 100 , 0.65, 1.29 = ° ≈ ≈ 9. B C b 56.8 , 23.2 , 4.25 ≈ ° ≈ ° ≈ 10. No triangle 11. b A C 3.32, 62.8 , 17.2 ≈ ≈ ° ≈ ° 12. A C c 36.2 , 63.8 , 4.55 ≈ ° ≈ ° ≈ 13. No triangle 14. A B C 83.3 , 44.0 , 52.6 ≈ ° ≈ ° ≈ ° 15. c A B 2.32, 16.1 , 123.9 ≈ ≈ ° ≈ ° 16. B C c 36.2 , 63.8 , 4.55 ≈ ° ≈ ° ≈ 17. A B C 39.6 , 18.6 , 121.9 ≈ ° ≈ ° ≈ ° 18. Two triangles: ≈ ° ≈ ° ≈ ≈ ° B C c B 13.4 , 156.6 , 6.86 or 166.6 , 1 1 1 2 C c 3.4 , 1.02 2 2 ≈ ° ≈ 19. b c C 11.52, 10.13, 60 ≈ ≈ ≈ ° 20. a B C 5.23, 46.0 , 64.0 ≈ ≈ ° ≈ ° 21. 1.93 22. 18.79 23. 6 24. 3.80 25. 0.32 26. 1.92 in.2 27. 48.2° and 41.8° 28. 23.32 ft 29. 2.15 mi 30. 132.55 ftmin 31. 12.7° 32. 29.97 ft 33. 6.22 mi 34. (a) 131.8 mi (b) 23.1° (c) 0.21 hr 35. 8798.67 sq ft 36. S4.0 E° 37. (a) 16.7 cθ = ° (b) 1.44 ft 38. (a) 5.7 cθ = ° ′ (b) 0.50 ft 39. d t t 3 cos 2 π( ) ( ) = − 40. (a) Simple harmonic (b) 6 ft (c) sec π (d) 1 oscillation sec π 41. (a) Simple harmonic (b) 2 ft (c) 2 sec (d) 1 2 oscillation sec Chapter Test (page 596) 1. sin 5 5 ; cos 2 5 5 ; tan 1 2 ; csc 5; sec 5 2 ; cot 2 θ θ θ θ θ θ = = = = = = 2. 0 3. a B C 15.88, 57.5 , 70.5 = ≈ ° ≈ ° 4. b C c 6.85, 117 , 16.30 ≈ = ° ≈ 5. A B C 52.4 , 29.7 , 97.9 ≈ ° ≈ ° ≈ ° 6. b c B 4.72, 1.67, 105 ≈ ≈ = ° 7. No triangle 8. c A B 7.62, 80.5 , 29.5 ≈ ≈ ° ≈ ° 9. 15.04 square units 10. 19.81 square units 11. 61.0° 12. 1.3° 13. The area of the shaded region is 9.26 cm .2 14. 54.15 square units 15. Madison will have to swim about 2.23 miles. 16. 12.63 square units 17. The lengths of the sides are 15, 18, and 21. 18. d t t d t 5sin42 sin 3 or 3.346 sin 3 π π ( ) ( ) ( ) ( ) = ° ≈ 42. (a) d t e t 15 cos 4 25 0.5625 6400 t 0.75 80 2π ( ) = − − ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ − (b) 15 215 25 0 43. (a) The motion is damped. The bob has mass m 20 kg = with a damping factor of 0.6 kg sec. (b) 15 m leftward 44. y 2 x y 5 2 sin x y 5 cos(2x) 2P (c) 15 215 25 0 (d) 13.92 m leftward (e) d 0 → Cumulative Review (page 597) 2. x y 5 1 9 2 2 ( ) ( ) + + − = y 5 x 1 (25, 1) 3. x x x 1 or 4 { } ≤− ≥ 4. y 3 x 2.5 5. y 2.5 x P 6. (a) 2 5 5 − (b) 5 5 (c) 4 5 − (d) 3 5 − (e) 5 5 10 − (f) 5 5 10 − + 7. (a) 0 0 4 60 (b) 1.5 21.5 4 0 (c) 10 250 4 0 (d) 0 0 4 8 1. 1 3 , 1 { } 8. (a) y 5 x 5 (b) y 10 x 5 (c) y 5 x 5 (d) y 5 x 5 (e) y 9 x 5 (f) y 5 x 8 (g) y 1.25 x 2P (h) y 1.25 x 2P (i) y 2 x P 9. Two triangles: A B b 59.0 , 81.0 , 23.05 1 1 1 ≈ ° ≈ ° ≈ or A B b 121.0 , 19.0 , 7.59 2 2 2 ≈ ° ≈ ° ≈ 10. i i 2, 2, 1 3 , 1, 2 { } −
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