468 CHAPTER 6 Trigonometric Functions The Chapter Test Prep Videos include step-by-step solutions to all chapter test exercises. These videos are available in MyLab™ Math. In Problems 1–3, convert each angle in degrees to radians. Express your answer as a multiple of π. 1. ° 260 2. − ° 400 3. ° 13 In Problems 4–6, convert each angle in radians to degrees. 4. π − 8 5. π9 2 6. π3 4 In Problems 7–12, find the exact value of each expression. 7. π sin 6 8. π π ( ) − − cos 5 4 cos 3 4 9. ( ) − ° cos 120 10. ° tan330 11. π π − sin 2 tan 19 4 12. ° − ° 2 sin 60 3cos45 2 In Problems 13–16, use a calculator to evaluate each expression. Round your answer to three decimal places. 13. ° sin17 14. π cos 2 5 15. ° sec229 16. π cot 28 9 17. Fill in each table entry with the sign of each function. θ sin θ cos θ tan θ sec θ csc θ cot θ in QI θ in QII θ in QIII θ in QIV 18. If ( ) = f x x sin and ( ) = f a 3 5 , find ( ) − f a . In Problems 19–21, find the value of the remaining five trigonometric functions of θ. 19. θ θ = sin 5 7 , in quadrant II 20. θ π θ π = < < cos 2 3 , 3 2 2 21. θ π θ π = − < < tan 12 5 , 2 In Problems 22–24, the point ( ) x y , is on the terminal side of angle θ in standard position. Find the exact value of the given trigonometric function. 22. θ ( ) 2, 7 , sin 23. θ ( ) −5, 11 , cos 24. θ ( ) − 6, 3 , tan In Problems 25 and 26, graph the function. 25. π ( ) = − y x 2 sin 3 6 26. π ( ) = − + + y x tan 4 2 27. Write an equation for a sinusoidal graph with the following properties: π π = − = = − A 3 Period 2 3 Phase shift 4 28. Logan has a garden in the shape of a sector of a circle; the outer rim of the garden is 25 feet long and the central angle of the sector is ° 50 . She wants to add a 3-foot-wide walk to the outer rim. How many square feet of paving blocks will she need to build the walk? 29. Hungarian Adrian Annus won the gold medal for the hammer throw at the 2004 Olympics in Athens with a winning distance of 83.19 meters.* The event consists of swinging a 16-pound weight attached to a wire 190 centimeters long in a circle and then releasing it. Assuming his release is at a ° 45 angle to the ground, the hammer will travel a distance of v g 0 2 meters, where = g 9.8 meters second2 and v 0 is the linear speed of the hammer when released. At what rate (rpm) was he swinging the hammer upon release? Chapter Test *Annus was stripped of his medal after refusing to cooperate with postmedal drug testing.
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