Chapter Test AN73 13. Limaçon without inner loop; symmetric with respect to the polar axis 3P 4 U 5 5P 4 U 5 3P 2 U 5 7P 4 U 5 P 2 U 5 P 4 U 5 y x 1 2 4 5 U 5 P U 5 0 P 2 4, (3, 0) (5, P) 3P 2 4, 14. i e 2 cos 5 4 sin 5 4 ; 2 i 5 4 π π ( ) + π ⋅ 15. i e 5 cos5.640 sin5.640 ; 5 i 5.640 ( ) + ⋅ 16. i 3 − + 2 22 Imaginary axis Real axis 2 22 17. i 3 2 3 3 2 − + 2 22 Imaginary axis Real axis 3 21 18. i 0.10 0.02 − 0.10 20.02 Imaginary axis Real axis 0.06 20.06 19. zw i e z w i e cos 13 18 sin 13 18 or ; cos 6 sin 6 or i i 13 18 6 π π π π = + = + π π ⋅ ⋅ 20. zw z w i e 6 or 6 ; 3 2 cos 8 5 sin 8 5 or 3 2 e i 8 5 i 0 π π ( ) = = + π ⋅ ⋅ 21. zw i e z w i e 5 cos 36 sin 36 or 5 ; 5 cos 12 sin 12 or 5 i i 36 12 π π π π ( ) ( ) = + = + π π ⋅ ⋅ 22. e i i 27 ; 27 cos 3 sin 3 ; 27 2 27 3 2 i 3 π π ( ) + + π⋅ 23. π π ( ) + π⋅ e i i 4 ; 4 cos 2 sin 2 ; 4 i 2 24. e i 64 ; 64 cos0 sin0 ; 64 i 0 ( ) + ⋅ 25. ( ) + − − ⋅ e i i 625 ; 625 cos3.709 sin3.709 ; 527 336 i 3.709 26. e e i i 3, 3 , 3 or 3, 3 2 3 3 2 , 3 2 3 3 2 i i 2 3 4 3 − + − − π π ⋅ ⋅ 27. v u u 1 v 28. 2u 1 3v 3v 2u 29. v i j v 2 4 ; 2 5 = − = 30. = − + = v i j v 3 ; 10 31. i j 2 2 − 32. i j 20 13 − + 33. 5 34. 5 5 7.24 + ≈ 35. i j 2 5 5 5 5 − + 36. v i j 3 2 3 3 2 = + 37. 120° 38. 43 6.56 ≈ 39. v i j k 3 5 3 = − + 40. i j k 21 2 5 − − 41. 38 42. 0 43. i j k 3 9 9 + + 44. 0 45. i j k i j k 19 19 3 19 19 3 19 19 or 19 19 3 19 19 3 19 19 + + − − − 46. v w 11; 169.7 θ ⋅ = − ≈ ° 47. v w 4; 153.4 θ ⋅ = − ≈ ° 48. v w 1; 70.5 θ ⋅ = ≈ ° 49. v w 0; 90 θ ⋅ = = ° 50. Parallel 51. Neither 52. Orthogonal 53. v i j v i j 4 5 3 5 ; 6 5 8 5 1 2 = − = + 54. v i j v i j 9 10 3 ; 7 10 21 10 1 2 ( ) = + = − + 55. 56.1 ; 138 ; 68.2 α β γ ≈ ° ≈ ° ≈ ° 56. 2 83 57. i j k 2 3 − + − 58. 0 59. 29 5.39 mph; ≈ 0.4 mi 60. Left cable: 1843.21 lb; right cable: 1630.41 lb 61. 50 ft-lb 62. A force of 697.2 lb is needed to keep the van from rolling down the hill. The magnitude of the force on the hill is 7969.6 lb. Chapter Test (page 678) 1–3. P 2 P 3 P 4 P 6 0 3P 4 2, P 3 24, P 6 3, 2 4. 4, 3 π ( ) 5. x y 49 2 2 + = 3P 4 U 5 5P 4 U 5 3P 2 U 5 7P 4 U 5 P 2 U 5 P 4 U 5 y x U 5 P U 5 0 6. y x 3 = or y x3 = 3P 4 U 5 5P 4 U 5 3P 2 U 5 7P 4 U 5 P 2 U 5 P 4 U 5 y x U 5 P U 5 0 7. y x 8 2 = 3P 4 U 5 5P 4 U 5 3P 2 U 5 7P 4 U 5 P 2 U 5 P 4 U 5 y x U 5 P U 5 0 8. r cos 5 2 θ = is symmetric about the pole, the polar axis, and the line 2 . θ π = 9. r 5 sin cos2 θ θ = is symmetric about the line 2 . θ π = The tests for symmetry about the pole and the polar axis fail, so the graph of r 5 sin cos2 θ θ = may or may not be symmetric about the pole or polar axis. 10. z w i e 6 cos 107 180 sin 107 180 ; 6 i 107 180 π π ( ) ⋅ = + π ⋅ 11. w z i e 3 2 cos 33 20 sin 33 20 ; 3 2 i 33 20 π π ( ) = + π ⋅ 12. w i e 243 cos 11 18 sin 11 18 ; 243 i 5 11 18 π π ( ) = + π ⋅
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