Inverse Trig Functions Inverse Functions The domain of

Inverse Trig Functions

Inverse Functions • The domain of the inverse is the range of the original function • The range of the inverse is the domain of the original function • Switching x and y

To determine whether the inverse is a function… • Switch x and y values and determine whether the domain of inverse is paired with only one value in the range (domain can not repeat)

Determining whether the inverse is a function from the graph of the original • You do the vertical line test to determine whether the graph represents a function • To determine whether its inverse would be a function, then you would do a horizontal line test

Finding the Inverse of a Relation What is the inverse of relation s? Relation s X Y 0 -1 2 0 3 2 4 3

To find the inverse of a function • • 1. 2. 3. 4. Notation: f -1(x)= Steps: Replace f(x) with y Switch the x and y variable Solve for y Replace y with f -1(x)=

Find the following

Find the following

Things to Remember! •

Inverse Sine Function The horizontal line test shows that the sine function is not one-to-one and has no inverse function.

The Restricted Domain •

Graph the Inverse Sine • x y -1 x -1 y -. 707 0 0. 707 1 1

Graph of Inverse Sine x -1 y 0. 707 1

Inverse Cosine Function • As with the sine, the domain must again be restricted. For cosine we restrict to

Graph the Inverse Cosine • x 0 y 1 x 1 . 707 0 0 -. 707 -1 -1 y 0

Graph of Inverse Cosine x 1. 707 0 -. 707 -1 y 0

Inverse Tangent Function •

Graph the Inverse Tangent x y und x und y -1 0 0 1 1 und

Graph of Inverse Tangent x und y 0 1 und

Graph of Inverse Cosecant •

Graph of Inverse Secant •

Graph of Inverse Cotangent •

Defined Domains

Evaluating Inverses •

Evaluate •

Evaluate •

Evaluate •

Evaluate •

Evaluate •

Evaluate •

Evaluate •

Evaluate •

Evaluate •

Evaluate •