chapter 8 - Chapter 8 Exercises 8.1 1. 30 = 30 radians =...

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253 Chapter 8 Exercises 8.1 1. 30 °= 30 π 180 radians = π 6 radians 120 120 π 180 radians = 2 π 3 radians 315 315 π 180 radians = 7 π 4 radians 2. 18 18 π 180 radians = π 10 radians 72 72 π 180 radians = 2 π 5 radians 150 150 π 180 radians = 5 π 6 radians 3. 450 450 π 180 radians = 5 π 2 radians 210 °= − 210 π 180 radians =− 7 π 6 radians 90 90 π 180 radians π 2 radians 4. 990 990 π 180 radians = 11 π 2 radians 270 270 π 180 radians 3 π 2 radians 540 540 π 180 radians 3 π radians 5. t = 8 π 2 = 4 π radians 6. t 3 π 2 3 π 2 radians 7. t = 7 π 2 = 7 π 2 radians 8. t = 9 π 2 = 9 π 2 radians 9. t 6 π 2 3 π radians 10. t 5 π 2 5 π 2 radians 11. t = 2 π 3 = 2 π 3 radians 12. t = 5 π 4 = 5 π 4 radians 13. 3 π 2 3 π 4 5 π 14. x y π 3 x y 5 π 2 x y 6 π
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Chapter 8: The Trigonometric Functions ISM: Calculus & Its Applications, 11e 254 15. π 3 3 π 4 7 π 2 16. x y π 4 x y 3 π 2 x y –3 π 17. π 6 2 π 3 π 18. x y 2 π 3 x y π 6 x y 7 π 2 Exercises 8.2 1. 13 sin ; cos 22 tt == 2. 25 sin ; cos 33 3. 32 1 3 rxy =+=+ = 23 sin ; cos 13 13 4. , so 41 1 5 xry =+ =−=− = 11 sin ; cos 44 5 5. 2 2 13 12 5 = −= − = sin t = 12 13 ; cos t = 5 13 6. 35 3 4 = 53 sin ; cos 34 34 7. (2 ) 1 5 =+= + = 12 sin ; cos 55
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ISM: Calculus & Its Applications, 11e Chapter 8: The Trigonometric Functions 255 8. 22 2 2 2( 3 ) 1 3 rxy =+=+ −= 32 sin ; cos 13 13 tt == 9. 2 2 (2 ) ( 2 ) 8 =+= += sin 2 82 2 t == = 2 cos 2 2 t − = 2 10. 2 2 (.6) (.8) 1 + = sin t = .8 1 = .8; cos t = .6 1 = .6 11. 2 2 (. 6 ) 8 ) 1 −+ sin t = 1 =− .8; cos t = 1 12. 2 2 (.8) ( .6) 1 + sin t = 1 .6; cos t = 1 = .8 13. a = 12, b = 5, and c = 13; sin t = b c = 5 13 = .3846 t = .3948 radians 14. t = 1.1 and c = 10.0; sin t = b c ; sin1.1 = b 10.0 b = .89121(10.0) = 8.9 15. t = 1.1 and b = 3.2; sin t = b c = 3.2 c c = 3.2 .89121 = 3.6 16. t = .4 and c = 5.0; cos t = a c ; cos.4 = a 5.0 a = (.92106)(5.0) = 4.6 17. t = .4, a = 10.0 cos .4 = 10.0 c ; c = 10.0 .92106 = 10.9 18. t = .9, c = 20.0; sin t = b c ; sin.9 = b 20.0 b = (.78333)(20.0) = 15.7 cos t = a c ; cos.9 = a 20.0 a = (.62161)(20) = 12.4 19. t = .5, a = 2.4 cos t = a c ; cos.5 = 2.4 c c = 2.4 .87758 = 2.7 sin t = b c ; sin.5 = b 2.73 b = (.47943)(2.73) = 1.3 20. t = 1.1, b = 3.5; sin t = b c = 3.5 c c = 3.5 .89121 = 3.9 cos t = a c ; cos1.1 = a 3.93 a = (.45360)(3.93) = 1.8 21. cos t = cos π 6 t = π 6 22. cos t = cos 3 π 2 t = π 2 23. cos t = cos 5 π 4 t = 3 π 4 24. cos t = cos 4 π 6 t = 2 π 3 25. cos t = cos 5 π 8 t = 5 π 8 26. cos t = cos 3 π 4 t = 3 π 4 27. sin t = sin 3 π 4 t = π 4 28. sin t = sin 7 π 6 t π 6 29. sin t = sin 4 π 3 t = π 3 30. sin t sin 3 π 8 t 3 π 8 31. sin t sin π 6 t π 6 32. sin t sin π 3 t = π 3
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Chapter 8: The Trigonometric Functions ISM: Calculus & Its Applications, 11e 256 33. sin t = cos t ; t = π 4 34. sin t =− cos t t π 4 35. cos t decreases from 1 to –1 as t increases from 0 to π . 36. As t increases from π to 3 π 2 , sin t decreases from 0 to –1. From 3 π 2 to 2 π , sin t increases from –1 to 0.
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This note was uploaded on 04/04/2010 for the course MATH MATH 16B taught by Professor Unknown during the Spring '10 term at UC Davis.

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chapter 8 - Chapter 8 Exercises 8.1 1. 30 = 30 radians =...

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