1. Inverse Trigonometric Functions Section 4.7

2. Objectives Evaluate inverse trigonometric functions at given values. State the domain and range of each of the inverse trigonometric functions. Use right triangles to find the composition of a trigonometric function and an inverse trigonometric function. Solve simple trigonometric equations requiring inverse trigonometric functions.

3. Vocabulary arcsine of a number arccosine of a number arctangent of a number arcsecant of a number

4. The graph of the function f(x) = sin(x) is not one-to-one

5. The restricted graph of the function f(x) = sin(x) is one-to- one

6. and thus has in inverse function What is the domain? What is the range?

7. The graph of the function f(x) = cos(x) is not one-to-one

8. The restricted graph of the function f(x) = cos(x) is one-to- one

9. and thus has in inverse function What is the domain? What is the range?

10. The graph of the function f(x) = tan(x) is not one-to-one

11. The restricted graph of the function f(x) = tan(x) is one- to-one

12. and thus has in inverse function What is the domain? What is the range?

13. Evaluate each of the following (remember that the output of an inverse trigonometric function is an angle) What angle between and has a sine value of 1? What angle between and has a sine value of -1/2? What angle between 0 and π has a cosine value of 0?

14. Evaluate each of the following (remember that the output of an inverse trigonometric function is an angle) What angle between and has a tangent value of ? What angle between and has a sine value of ? What angle between 0 and π has a cosine value of -1?

15. Evaluate each of the following

18. Rewrite the expression as an algebraic expression in x