736 CHAPTER 7 Trigonometric Identities and Equations 8. Consider the inverse cosine function y = cos-1 x, or y = arccos x. (a) What is its domain? (b) What is its range? (c) Is this function increasing or decreasing? (d) arccos A - 1 2B = 2p 3 . Why is arccos A - 1 2B not equal to - 4p 3 ? 9. Consider the inverse tangent function y = tan-1 x, or y = arctan x. (a) What is its domain? (b) What is its range? (c) Is this function increasing or decreasing? (d) Is there any real number x for which arctan x is not defined? If so, what is it (or what are they)? 10. Give the domain and range of each inverse trigonometric function, as defined in this section. (a) inverse cosecant function (b) inverse secant function (c) inverse cotangent function 11. Concept Check Why are different intervals used when restricting the domains of the sine and cosine functions in the process of defining their inverse functions? 12. Concept Check For positive values of a, cot-1 a is calculated as tan-1 1 a. How is cot-1 a calculated for negative values of a? Find the exact value of each real number y if it exists. Do not use a calculator. See Examples 1 and 2. 13. y = sin-1 0 14. y = sin-11-12 15. y = cos-11-12 16. y = arccos 0 17. y = tan-1 1 18. y = arctan1-12 19. y = arctan 0 20. y = tan-11-232 21. y = arcsin ¢- 23 2 ≤ 22. y = sin-1 22 2 23. y = arccos ¢- 23 2 ≤ 24. y = cos-1 a- 1 2b 25. y = sin-1 23 26. y = arcsin A -22 B 27. y = cot-11-12 28. y = arccot A -23 B 29. y = csc-11-22 30. y = csc-1 22 31. y = arcsec 223 3 32. y = sec-1 A -22 B 33. y = sec-1 1 34. y = sec-1 0 35. y = csc-1 22 2 36. y = arccsc a- 1 2b Find the degree measure of u if it exists. Do not use a calculator. See Example 3. 37. u = arctan1-12 38. u = tan-1 23 39. u = arcsin ¢- 23 2 ≤ 40. u = arcsin ¢- 22 2 ≤ 41. u = arccos a- 1 2b 42. u = sec-11-22 43. u = cot-1 a- 23 3 b 44. u = cot-1 23 3 45. u = csc-11-22 46. u = csc-11-12 47. u = sin-1 2 48. u = cos-11-22
RkJQdWJsaXNoZXIy NjM5ODQ=