1. INVERSE TRIGONOMETRIC FUNCTIONS

2. DEFINITION: If is a one-to-one function with domain A and range B, then its inverse is the function with domain B and range A defined by For a function to have an inverse, it must be one-to-one. Since the trigonometric functions are not one-to-one, they do not have inverses. It is possible, however, to restrict the domains of the trigonometric functions in such a way that the resulting functions are one-to-one.

3. Inverse trigonometric functions are defined as follows: y x o y = sinx y x y = sin-1 x

4. y x o y = cosx y x y = cos-1 x

5. y x o y = tanx y x y = tan-1 x

6. y x o y = cotx y x y = cot-1 x

7. y x o y = secx y x y = sec-1 x

8. y x o y = cscx y x y = csc-1 x

9. EXAMPLE: Find the exact values of the following:

12. II. Solve for x:

13. EXERCISES: Find the exact values of the following: