# Chapter 4: Inverse Trigonometric Functions

**At Grade**Created by: CK-12

## Introduction

In this Chapter you'll learn how to find the inverse of trigonometric functions. An inverse function is a function that "undoes" another function. For example, the inverse of multiplying by three is dividing by three.

Trigonometric functions deal with relationships between sides of a triangle. And since they are functions of a angle, applying the inverse trigonometric function will give back the original angle under consideration.

Here you'll learn to find inverse functions, graph them, and apply them.

## Chapter Outline

- 4.1. Definition of the Inverse of Trigonometric Ratios
- 4.2. Exact Values for Inverse Sine, Cosine, and Tangent
- 4.3. Inverse of Functions through Algebraic Manipulation
- 4.4. Inverses by Mapping
- 4.5. Inverses of Trigonometric Functions
- 4.6. Composition of Trig Functions and Their Inverses
- 4.7. Definition of Inverse Reciprocal Trig Functions
- 4.8. Composition of Inverse Reciprocal Trig Functions
- 4.9. Trigonometry in Terms of Algebra
- 4.10. Applications of Inverse Trigonometric Functions

### Chapter Summary

## Summary

This Chapter discussed inverse trigonometric functions, including how to find them through graphing and algebraic means. Once the inverse functions were found, information about how to find compositions of inverse trig functions and inverse reciprocal functions were discussed. These topics were then presented in terms of Algebra.

The Chapter concluded with applications of inverse trig functions to real life situations.