LHS CAT4e ISM-06-final

LHS CAT4e ISM-06-final - Chapter 6 THE CIRCULAR FUNCTIONS...

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533 Chapter 6 THE CIRCULAR FUNCTIONS AND THEIR GRAPHS Section 6.1: Radian Measure 1. Since θ is in quadrant I, 0. 2 π << Since 1.57, 2 1 is the only integer value in the interval. Thus, the radian measure of is 1 radian. 2. Since is in quadrant II, . 2 θπ Since 1.57 and 3.14, 2 ≈≈ 2 and 3 are the only integers in the interval. Since is closer to , 2 the radian measure of is 2 radians. 3. Since is in quadrant II, . 2 Since 1.57 and 3.14, 2 2 and 3 are the only integers in the interval. Since is closer to , the radian measure of is 3 radians. 4. Since is an angle in quadrant IV drawn in a clockwise direction, 0. 2 −<< Also 1.57, 2 −≈ and –1 is the only integer in the interval. Thus, the radian measure of is –1 radian. 5. Since is an angle in quadrant III drawn in a clockwise direction, . 2 πθ Also 3.14 and 1.57, 2 so –2 and -3 are the only integers in the interval. is closer to , so the radian measure of is –3 radians. 6. Since is an angle in quadrant III drawn in a clockwise direction, . 2 Also 3.14 and 1.57, 2 so –2 and -3 are the only integers in the interval. is closer to 2 , so the radian measure of is –2 radians. 7. 60 60 radian radians 180 3 ππ ⎛⎞ °= = ⎜⎟ ⎝⎠ 8. 30 30 radian radians 180 6 = 9. 90 90 radian radians 180 2 = 10. 2 120 120 radian radians 180 3 = 11. 5 150 150 radian radians 180 6 = 12. 3 270 270 radian radians 180 2 = 13. 5 300 300 radian radians 180 3 °=− =− 14. 7 315 315 radian radians 180 4 15. 5 450 450 radian radians 180 2 = 16. 8 480 480 radian radians 180 3 = 17. 1800 1800 radian 10 radians 180 ° = ° 18. 3600 3600 radian 180 20 radians −° = ° 19. Multiply the degree measure by radian 180 and reduce. Your answer will be in radians. Leave the answer as a multiple of , unless otherwise directed.
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534 Chapter 6: The Circular Functions and Their Graphs 20. Multiply the radian measure by 180 π ° and reduce. Your answer will be in degrees. 21.-24. Answers will vary. 25. 180 60 33 ππ ° ⎛⎞ == ° ⎜⎟ ⎝⎠ 26. 88 1 8 0 480 ° ° 27. 77 1 8 0 315 44 ° ° 28. 22 1 8 0 120 ° ° 29. 11 11 180 330 66 ° ° 30. 15 15 180 675 ° ° 31. 180 30 ° −= = −° 32. 1 8 0 288 55 ° = ° 33. 1 8 0 126 10 10 ° ° 34. 11 11 180 132 15 15 ° ° 35. 4 4 180 48 15 15 ° = ° 36. 7 7 180 63 20 20 ° = ° 37. 17 17 180 153 20 20 ° ° 38. 11 11 180 66 30 30 ° ° 39. 180 9 0 0 ° = 40. 180 15 15 2700 ° ° 41. 39 39 radian .68 radian 180 °= 42. 74 74 radian 1.29 radians 180 43. 42.5 42.5 radian .742 radians 180 44. 264.9 264.9 radian 4.623 radians 180 45. ( ) 10 60 139 10 139 139.1666667 radian 180 2.43 radians 46. ( ) 50 60 174 50 174 174.8333333 radian 180 3.05 radians 47. 64.29 64.29 radian 1.122 radians 180 48. 85.04 85.04 radian 1.484 radians 180 49. ( ) 25 60 56 25 56 56.41666667 radian 180 .9847 radians 50. ( ) 37 60 122 37 122 122.61666667 radian 180 2.140 radians 51. 47.6925 47.6925 radian 180 .832391 radian 52. 23.0143 23.0143 radian 180 .401675 radian 53. () 180 2 radians 2 114.591559 114 .591559 60 114 35 ° =≈ ° + ≈°
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Section 6.1: Radian Measure 535 54. () 180 5 radians 5 286.4788976 286 .4788976 60 286 29 π ° ⎛⎞ =≈ ° ⎜⎟ ⎝⎠ + ≈° 55.
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This note was uploaded on 11/13/2010 for the course MATH MAT 123 taught by Professor Smith during the Spring '10 term at Thomas Edison State.

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LHS CAT4e ISM-06-final - Chapter 6 THE CIRCULAR FUNCTIONS...

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