466 CHAPTER 6 Trigonometric Functions Review Exercises In Problems 1 and 2, convert each angle in degrees to radians. Express your answer as a multiple of π. 1. ° 135 2. ° 18 In Problems 3 and 4, convert each angle in radians to degrees. 3. π3 4 4. π − 5 2 In Problems 5–15, find the exact value of each expression. Do not use a calculator. 5. π π − tan 4 sin 6 6. π ° − 3sin45 4 tan 6 7. π π ( ) + − 6cos 3 4 2tan 3 8. π π ( ) ( ) − − − sec 3 cot 5 4 9. π π + tan sin 10. ( ) ° − − ° cos540 tan 405 11. ° + ° sin 20 1 sec 20 2 2 12. ° ° sec50 cos50 13. ( ) − ° ° cos 40 cos40 14. ( ) − ° ° sin 40 sin40 −1 15. ( ) ° − ° sin310 csc 50 In Problems 16–23, find the exact value of each of the remaining trigonometric functions. 16. θ θ = sin 4 5 , is acute 17. θ θ = < tan 12 5 , sin 0 18. θ θ = − < sec 5 4 , tan 0 19. θ θ = sin 12 13 , in quadrant II 20. θ π θ π = − < < sin 5 13 , 3 2 2 21. θ θ = ° < < ° tan 1 3 , 180 270 22. θ π θ π = < < sec 3, 3 2 2 23. θ π θ π = − < < cot 2, 2 In Problems 24–32, graph each function. Each graph should contain at least two periods. Use the graph to determine the domain and the range of each function. 24. ( ) = y x 2sin 4 25. ( ) = − y x 3cos 2 26. π ( ) = + y x tan 27. ( ) = − y x 2tan 3 28. π ( ) = + y x cot 4 29. ( ) = y x 4sec 2 30. π ( ) = + y x csc 4 31. ( ) = + − y x 4sin 2 4 2 32. π ( ) = − y x 5cot 3 4 In Problems 33 and 34, determine the amplitude and period of each function without graphing. 33. ( ) = y x sin 2 34. π ( ) = − y x 2cos 3 In Problems 35–38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods. 35. ( ) = y x 4sin 3 36. π ( ) = − + y x cos 1 2 2 37. π ( ) = − y x 1 2 sin 3 2 38. π( ) = − − y x 2 3 cos 6 39. x y 24p 4p 8p 25 5 40. x y 2422 2 4 6 8 10 27 7 In Problems 39 and 40, find a function whose graph is given.
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