Study Guide

The Unit Circle

The Unit Circle Introduction

As a battle-scarred veteran of Geometry, you already know a bit of trigonometry from working with triangles. Trigonometry, though, is more about angles than it is about the triangles themselves, so it is useful in many different settings in math. We're going to see that in this unit using the unit circle. We'll learn more about circles, more about trig, and maybe even more about ourselves. Get ready for a journey of self-discovery and adventure as we—pffffft, we couldn't finish that with a straight face. Yeah, this stuff won't change your life, but it will teach you something about solving trigonometric equations.

The Unit Circle Resources

Websites

Sporcle: Can You Name the Simple Degree to Radian Conversions?
Well? CAN YOU? (Our bet is on, "Yes.")

Trigonometry for You: Function Values Quiz
There are 15 questions about the sine, cosine, and tangent of different angles. There's no pressure, no time limit, and a happy smiley face when you get it right. Daww.

Math Is Fun: Even and Odd functions
Just because a function is a little…odd, doesn't mean you can't be friends. Learn a bit about them, and maybe they won't seem so weird. Oh, and some functions are even, or not odd nor even; click the link, and maybe see what's up with that.

Videos

Patrick Just Math Tutorials: A Way to Remember the Entire Unit Circle for Trigonometry
Our pal Patrick sweetly talks us through remembering all the standard angles for the unit circle. We're getting sleepy from his dulcet tone…and more knowledgeable.

Find the Reference Angle (Radians) – Quick Explanation
Quick—you only have 6 minutes to find the corresponding acute angle of . Spend 5 minutes watching this video, then use the last minute doing what it tells you to find the angle.

Solving Basic Trigonometric Equations
In this video, a poor, defenseless trigonometric equation is meticulously and methodically picked apart for your education.

Matheatre: Unit Circle Trigonometry Song
We have a weak spot for good time-lapse videos. Add in a catchy math song, and we are hooked.

Games and Tools

Interactive Unit Circle
Drag the line around the unit circle to see what that angle is in both degrees and radians. Every time you go a full 360 degrees around, the red spiral grows ever larger. Did you know that 30,000 degrees equals ? We just can't stop spinning it around.

Purpose Games: Angles of the Unit Circle
There are 16 standard angles on a unit circle. How fast can you identify each one? Beat the high score and win a fabulous not-prize. *Note: not-prize has a value of no-value. Not available in stores.*

Mathway: Trigonometry Problem Solver
A website capable of solving trig equations? We are this freaking close to Skynet, it's frightening.