678 CHAPTER 6 The Circular Functions and Their Graphs Solve each problem. 15. Determine the six exact circular function values of s in the figure. 16. Do each of the following. (a) Use a calculator to approximate s in the interval C 0, p 2 D if sin s = 0.8258 . (b) Find the exact value of s in the interval C 0, p 2 D if cos s = 1 2 . 17. Angular and Linear Speed of a Point Suppose that point P is on a circle with radius 60 cm, and ray OP is rotating with angular speed p 12 radian per sec. (a) Find the angle generated by P in 8 sec. (b) Find the distance traveled by P along the circle in 8 sec. (c) Find the linear speed of P. x y s = 7 6 P x2 + y2 = 1 0 (1, 0) (–1, 0) (0, 1) (0, –1) Empty Full 1 in. 2 Find each exact function value. 9. sin 3p 4 10. cos a- 7p 6 b 11. tan 3p 2 12. sec 8p 3 13. tan p 14. cos 3p 2 8. Rotation of Gas Gauge Arrow The arrow on a car’s gasoline gauge is 1 2 in. long. See the figure. Through what angle does the arrow rotate when it moves 1 in. on the gauge? Convert each degree measure to radians. 1. 120° 2. -45° 3. 5° (to the nearest thousandth) Convert each radian measure to degrees. 4. 3p 4 5. - 7p 6 6. 4 (to the nearest minute) Solve each problem. 7. A central angle of a circle with radius 150 cm intercepts an arc of 200 cm. Find each measure. (a) the radian measure of the angle (b) the area of a sector with that central angle Chapter 6 Test
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