756 CHAPTER 7 Trigonometric Identities and Equations CHECK A check is necessary because we squared each side when solving the equation. arcsin x - arccos x = p 6 Original equation arcsin 23 2 - arccos 23 2 ≟p 6 Let x = 23 2 . p 3 - p 6 ≟p 6 Substitute inverse values. p 6 = p 6 ✓ True The solution set is U 23 2 V . S Now Try Exercise 39. 7.7 Exercises CONCEPT PREVIEW Answer each question. 1. Which one of the following equations has solution 0? A. arctan 1 = x B. arccos 0 = x C. arcsin 0 = x 2. Which one of the following equations has solution p 4? A. arcsin 22 2 = x B. arccos a- 22 2 b = x C. arctan 23 3 = x 3. Which one of the following equations has solution 3p 4 ? A. arctan 1 = x B. arcsin 22 2 = x C. arccos a- 22 2 b = x 4. Which one of the following equations has solution - p 6? A. arctan 23 3 = x B. arccos a- 1 2b = x C. arcsin a- 1 2b = x 5. Which one of the following equations has solution p? A. arccos1-12 = x B. arccos 1 = x C. arcsin1-12 = x 6. Which one of the following equations has solution - p 2? A. arctan1-12 = x B. arcsin1-12 = x C. arccos1-12 = x CAUTION When solving equations involving inverse trigonometric functions, pay careful attention to restrictions on domains and ranges. The following equations have no solutions. arcsin x = 3p 4 3p 4 is not in the range of the inverse sine function. cos-1 x = sin-1 2 2 is not in the domain of the inverse sine function.
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