1. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall

2. Chapter 14 Trigonometric Functions

3. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 14.7 Inverse Trigonometric Functions

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7. Example Find the exact value of Solution 1. We must find angle , whose sine equals 2. Rewrite continued

8. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 3. Use the exact value table to find the value of  that satisfies sin  = x. We conclude that

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12. Example Find the exact value of Solution 1. We must find angle , whose cosine equals 2. Rewrite 3. Use the exact value table to find the value of  that satisfies cos  = x.

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16. Example Find the exact value of Solution 1. We must find angle , whose tangent equals 2. Rewrite 3. Use the exact value table to find the value of  that satisfies tan  = x.

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18. Example Find the exact value, if possible. Solution The inverse property applies for To evaluate observe that x = 0.6. Which lies in the domain of the inverse cosine function.

19. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example Find the exact value, if possible. Solution Let  represent an angle in whose tangent is 5/12. Use the definition of inverse tangent. Tan  is positive,  must be and angle in continued

20. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Find the exact value, if possible.

21. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Example If 0 < x ≤ 1, write as an algebraic expression in x. Solution Let  represent an angle in whose sine is x. Sin  is positive,  must be in the first quadrant. continued

22. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall If 0 < x ≤ 1, write as an algebraic expression in x.