Section 5.5 Inverse Trigonometric Functions & Their Graphs Chapter 5 – Trigonometric Functions: Unit Circle Approach Section 5.5 Inverse Trigonometric Functions & Their Graphs 5.5 - Inverse Trigonometric Functions & Their Graphs

Review of Inverse Functions Remember If the graph passes the horizontal line test, then the function has an inverse functions. If a point (a, b) is on the graph of f, then the point (b, a) is on the graph of f -1. The graph of f -1 is a reflection of the graph of f about the line y=x. 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Sine Function Does not pass the horizontal line test. Must restrict the domain to create an inverse function. 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Definition The inverse sine function is the function sin-1 with domain [-1, 1] and range [- ⁄ 2,  ⁄ 2] defined by The inverse sine function is also called arcsine denoted by arcsin. 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Note 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Graph of Inverse sine 5.5 - Inverse Trigonometric Functions & Their Graphs

Cancellation Properties - Sine Thus y = sin-1x is the number in the interval [- ⁄ 2,  ⁄ 2] whose sine is x. In other words we have the following: 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Examples Find the exact value of the following: 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Cosine Function Does not pass the horizontal line test. Must restrict the domain to create an inverse function. 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Definition The inverse cosine function is the function cos-1 with domain [-1, 1] and range [0, ] defined by The inverse sine function is also called arccosine denoted by arccos. 5.5 - Inverse Trigonometric Functions & Their Graphs

Graph of Inverse Cosine 5.5 - Inverse Trigonometric Functions & Their Graphs

Cancellation Properties - Cosine Thus y = cos-1x is the number in the interval [0, ] whose cosine is x. In other words we have the following: 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Examples Find the exact value of the following: 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Tangent Function Does not pass the horizontal line test. Must restrict the domain to create an inverse function. 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Definition The inverse tangent function is the function tan-1 with domain (-∞, ∞) and range (- ⁄ 2,  ⁄ 2) defined by The inverse tangent function is also called arctangent denoted by arctan. 5.5 - Inverse Trigonometric Functions & Their Graphs

Graph of Inverse Tangent 5.5 - Inverse Trigonometric Functions & Their Graphs

Cancellation Properties - Tangent Thus y = tan-1x is the number in the interval (- ⁄ 2,  ⁄ 2) whose sine is x. In other words we have the following: 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Examples Find the exact value of the following: 5.5 - Inverse Trigonometric Functions & Their Graphs

Evaluating Compositions 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Inverse Properties 5.5 - Inverse Trigonometric Functions & Their Graphs

Using Inverse Properties Evaluate the following: 5.5 - Inverse Trigonometric Functions & Their Graphs

5.5 - Inverse Trigonometric Functions & Their Graphs Examples – pg. 412 Find the exact value of the expression if it is defined. 5.5 - Inverse Trigonometric Functions & Their Graphs