672 CHAPTER 6 The Circular Functions and Their Graphs Convert each degree measure to radians. Leave answers as multiples of p. 5. 45° 6. 120° 7. 175° 8. 330° 9. 800° 10. 1020° Solve each problem. Use a calculator as necessary. 21. Arc Length The radius of a circle is 15.2 cm. Find the length of an arc of the circle intercepted by a central angle of 3p 4 radians. 22. Arc Length Find the length of an arc intercepted by a central angle of 0.769 radian on a circle with radius 11.4 cm. 23. Angle Measure Find the measure (in degrees) of a central angle that intercepts an arc of length 7.683 cm in a circle of radius 8.973 cm. 24. Angle Measure Find the measure (in radians) of a central angle whose sector has area 50p 3 cm2 in a circle of radius 10 cm. 25. Area of a Sector Find the area of a sector of a circle having a central angle of 21° 40′ in a circle of radius 38.0 m. 26. Area of a Sector A central angle of 7p 4 radians forms a sector of a circle. Find the area of the sector if the radius of the circle is 28.69 in. Find each exact function value. 31. tan p 3 32. cos 2p 3 33. sin a- 5p 6 b 34. tan a- 7p 3 b 35. csc a- 11p 6 b 36. cot1-13p2 Convert each radian measure to degrees. 11. 5p 4 12. 9p 10 13. 8p 3 14. 6p 5 15. - 11p 18 16. - 21p 5 Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 2 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of p. 17. 15 min 18. 20 min 19. 3 hr 20. 8 hr 2 in. 12 6 3 1 2 11 7 5 10 4 8 9 Distance between Cities Assume that the radius of Earth is 6400 km. 27. Find the distance in kilometers between cities on a north-south line that are on latitudes 28° N and 12° S, respectively. 28. Two cities on the equator have longitudes of 72° E and 35° W, respectively. Find the distance in kilometers between the cities. Concept Check Find the measure of each central angle u (in radians) and the area of each sector. 29. 2 1.5 U 30. 8 4 U
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