# Activities

• ##### Download

• • ##### Subject Area

• Math: Precalculus: Trigonometry (Triangle and Circular Functions)

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.9

## The Unit Circle

#### Activity Overview

Students will be able to describe the relationship between the unit circle and the sine and cosine functions. They will be also able to describe the shape of the sine and cosine curves after "unwrapping" the unit circle.

#### Objectives

• Students will describe the relationship between the unit circle and the sine and cosine functions.
• Students will describe the shape of the sine and cosine curves after unwrapping the unit circle.

#### Vocabulary

• continuous function
• periodic function
• unit circle

#### About the Lesson

This lesson involves using a slider to change the measure of the central angle of a unit circle and making connections with right triangle trigonometry.
As a result, students will:

• Discover the relationships between the right triangle and the line segments creating the sine and cosine functions.
• Observe that as the measure of the central angle changes line segments representing the length of a highlighted leg of the right triangle in the unit circle appear on the screen.
• Need prerequisite knowledge of right triangle trigonometry and continuous functions.