Solutions for Inverse Trigonometric Functions
Solutions to Try Its
1. 2. a. ; b. c. d. 3. 1.9823 or 113.578° 4. radians 5. 6. 7. 8. 9.Solutions to Odd-Numbered Exercises
1. The function is one-to-one on ; thus, this interval is the range of the inverse function of . The function is one-to-one on [0,π]; thus, this interval is the range of the inverse function of . 3. is the radian measure of an angle between and whose sine is 0.5. 5. In order for any function to have an inverse, the function must be one-to-one and must pass the horizontal line test. The regular sine function is not one-to-one unless its domain is restricted in some way. Mathematicians have agreed to restrict the sine function to the interval so that it is one-to-one and possesses an inverse. 7. True. The angle, that equals , will be a second quadrant angle with reference angle, , where equals . Since is the reference angle for , 9. 11. 13. 15. 17. 1.98 19. 0.93 21. 1.41 23. 0.56 radians 25. 0 27. 0.71 29. −0.71 31. 33. 0.8 35. 37. 39. 41. 43. 45. 47. t 49. domain [−1,1]; range [0,π]
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