615 6.2 The Unit Circle and Circular Functions CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. As necessary, refer to the figure that shows point P moving at a constant speed along the unit circle. x y s r u O B (1, 0) P P moves at a constant speed along the unit circle. (0, 1) (0, −1) (−1, 0) 7. The measure of how fast the position of point P is changing is the . 8. The measure of how fast angle POB is changing is the . 9. If the angular speed of point P is 1 radian per sec, then P will move around the entire unit circle in sec. 10. If the angular speed of point P is p radians per sec, then the linear speed is unit(s) per sec. 11. An angular speed of 1 revolution per min on the unit circle is equivalent to an angular speed, v, of radians per min. 12. If P is rotating with angular speed p 2 radians per sec, then the distance traveled by P in 10 sec is units. Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1. 13. s = p 2 14. s = p 15. s = 2p 16. s = 3p 17. s = -p 18. s = - 3p 2 Find each exact function value. See Example 2. 19. sin 7p 6 20. cos 5p 3 21. tan 3p 4 22. sec 2p 3 23. csc 11p 6 24. cot 5p 6 25. cos a- 4p 3 b 26. tan a- 17p 3 b 27. cos 7p 4 28. sec 5p 4 29. sin a- 4p 3 b 30. sin a- 5p 6 b 31. sec 23p 6 32. csc 13p 3 33. tan 5p 6 34. cos 3p 4 Find a calculator approximation to four decimal places for each circular function value. See Example 3. 35. sin 0.6109 36. sin 0.8203 37. cos1-1.15192 38. cos1-5.28252 39. tan 4.0203 40. tan 6.4752 41. csc1-9.49462 42. csc 1.3875 43. sec 2.8440 44. sec1-8.34292 45. cot 6.0301 46. cot 3.8426
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