# 5.1: What’s your Inverse?

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

*This activity is intended to supplement Trigonometry, Chapter 4, Lesson 3.*

**Time Required: 30 minutes**

## Activity Overview

This activity is intended to be teacher-led, where students will use their graphing calculators to graph the six inverse trig functions. The inverse reciprocal properties will be derived as a class.

**Topics Covered**

- Graphing inverses
- Finding the inverse of a function

**Teacher Preparation and Notes**

- Make sure students have cleared
Y= menu before starting. - Students will need to know how to find the inverse of a function algebraically. It might be helpful to have a warm-up covering this topic as a quick review.
- Go over the definition of a restricted domain and make sure students understand why they are necessary to find the inverse of trigonometric functions.
- Make sure students’ calculators are in
**Radians**.

**Associated Materials**

- Student Worksheet: What's your Inverse http://www.ck12.org/flexr/chapter/9702

## Problem 1

For the domain and range of

## Problem 2

Again, review the domain and range of

## Problem 3

The domain of

**For secant, cosecant and cotangent guide students through how to derive the equation that is needed to plug into the calculator.**

## Problem 4

Prove *Walk students through these steps*.

This means that

In

## Problem 5

Prove *Walk students through these steps*.

This means that

In

## Problem 6

Tangent and cotangent have a slightly different relationship. Recall that the graph of cotangent differs from tangent by a reflection over the

This means that

Because tangent is an odd function, or

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