Course: Trigonometry
Topic: Circular Functions
Subtopic: The Unit Circle


The unit circle developed in this section is probably the most widely useful item in all of trigonometry. It provides an easy way to know the trig functions of all the "nice" angles from 0° to 360°. It will be used throughout the rest of this class, calculus, and differential equations. The Unit Circle - understand it, memorize it, use it!


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: unit circle

Mini-Lectures and Examples

STUDY: The Unit Circle

Supplementary Resources (recommended)

Download/Print: THE UNIT CIRCLE

You must MEMORIZE the Unit Circle and NOT refer to it during a test!

Below are some sites that may help you to memorize the Unit Circle. A variety of "tricks" are included. Hopefully one "clicks" with you.

If you have an iPhone then download the free Trigo - Trig Bingo app to practice unit circle values.

Print this blank Unit Circle and see if you can fill-it out from memory. Great self-check :)

Supplemental Resources (optional)

Videos: Example:  Determine the Quadrant of the Terminal Side of An Angle Given Trig Function Signs

Determine Trigonometric Function Values using the Unit Circle
Properties of Trig Functions:  Domain, Range, and Sign in each Quadrant
Examples:  Determine Exact Trig Function Values With the Angle in Radians Using the Unit Circle
Example:  Determine the Domain of the Secant and Cosecant Functions Using the Unit Circle

rev. 2020-10-10