SECTION 7.1 The Inverse Sine, Cosine, and Tangent Functions 483 y x sin 1 = − if and only if x y sin . = π = = x x sin 3 3 2 The solution set is { } 3 2 . Now Work PROBLEM 71 Skill Building In Problems 11–26, find the exact value of each expression. 11. − sin 01 12. − cos 11 13. ( ) − − sin 1 1 14. ( ) − − cos 1 1 15. − tan 01 16. ( ) − − tan 1 1 17. − sin 2 2 1 18. − tan 3 3 1 19. − tan 3 1 20. − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ − sin 3 2 1 21. − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ − cos 3 2 1 22. − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ − sin 2 2 1 23. − cos 2 2 1 24. ( ) − − cos 1 2 1 25. − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ − tan 3 3 1 26. − sin 1 2 1 In Problems 27–38, use a calculator to find the approximate value of each expression rounded to two decimal places. 27. − sin 0.1 1 28. − cos 0.6 1 29. − tan 51 30. − tan 0.2 1 31. − cos 7 8 1 32. − sin 1 8 1 33. ( ) − − tan 0.4 1 34. ( ) − − tan 3 1 35. ( ) − − sin 0.12 1 36. ( ) − − cos 0.44 1 37. − cos 2 3 1 38. − sin 3 5 1 In Problems 39–62, find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator. 39. π ( ) − cos cos 4 5 1 40. π ( ) ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ − sin sin 10 1 41. π ( ) ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ − tan tan 3 8 1 42. π ( ) ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ − sin sin 3 7 1 43. π ( ) − sin sin 9 8 1 44. π ( ) − sin sin 11 4 1 45. π ( ) ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ − cos cos 5 3 1 46. π ( ) − cos cos 7 6 1 5. = − y x sin 1 if and only if , where − ≤ ≤ x 1 1 and π π − ≤ ≤ y 2 2 . 6. ( ) = − x x cos cos 1 for all numbers x for which . 7. True or False The domain of = − y x cos 1 is − ≤ ≤ x 1 1. 8. True or False ( )= − sin sin 0 0 1 and ( )= − cos cos 0 0. 1 9. True or False = − y x tan 1 if and only if = x y tan , where −∞< <∞ x and π π − < < y 2 2 . 10. Multiple Choice ( ) = − x x sin sin 1 for all numbers x for which (a) −∞< <∞ x (b) π ≤ ≤ x 0 (c) − ≤ ≤ x 1 1 (d) π π − ≤ ≤ x 2 2 Concepts and Vocabulary 7.1 Assess Your Understanding 3. True or False The graph of = y x cos is decreasing on the interval π [ ] 0, . (pp. 429–430) 4. π = tan 4 ; π = sin 3 ; π ( ) − = sin 6 ; π = cos . (pp. 398–405) 1. What are the domain and the range of = y x sin ? (pp. 413–414) 2. If the domain of a one-to-one function is [ )∞ 3, , the range of its inverse is . (p. 286) ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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