4.7 Inverse Trigonometric Functions 1

Recall: Inverse Functions O When does a function have an inverse? 2

Recall: Inverse Functions O Does the sine function have an inverse? 3

Definition of Inverse Sine Function O The inverse sine function is defined by O Domain: O Range: 4

Definition of Inverse Trig Functions 5

Examples If possible, find the exact value. 6

Compositions of Functions O What happens when you find the composition of a function with it’s inverse? 7

Compositions of Functions: Inverse Properties 8

Warning! O The inverse properties do not apply for arbitrary values of x and y!!! Example: 9

Examples: Using Inverse Properties If possible, find the exact value. 10

Examples: Compositions of Functions Find the exact value. 11

Examples: Compositions of Functions Write as an algebraic expression in x. 12