Precalculus: 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.