# Inverse Trigonometric Functions

## Module Overview

Inverse Trigonometric Functions - domain, range, graph, one-to-one function, applications, periodic functions

**TMM 002 PRECALCULUS (Revised March 21, 2017)**

**1. Functions: **

**1a.**Analyze functions. Routine analysis includes discussion of domain, range, zeros, general function behavior (increasing, decreasing, extrema, etc.), as well as periodic characteristics such as period, frequency, phase shift, and amplitude. In addition to performing rote processes, the student can articulate reasons for choosing a particular process, recognize function families and anticipate behavior, and explain the implementation of a process (e.g., why certain real numbers are excluded from the domain of a given function).*

# Section 1: Inverse Trigonometric Functions

We now study the inverse of trigonometric functions. Owing to the periodic nature these functions are not one-to-one functions. Thus their domains have to be suitably restricted so as to determine their inverses. Once this is done we can solve trigonometric equations using inverse functions.

**Review: **

- General properties of a one-to-one function and its inverse
- Domain, Range and fundamental cycle graphs of the six trigonometric functions
- Given the graph of a function draw the graph of the inverse.

**Learning Objectives:**

- The arcCosine and arcSine functions
- The arcTangent and arcCotangent functions
- The arcSecant and arcCosecant functions
- Domain, range and graphs
- Solving trigonometric equations.