This is a Flash animation I created to help students study and learn the Unit Circle. It's probably most useful to pre-calculus and trigonometry students, but many other students will find it helpful as well. It has many features, so play around with it to see how it works. There are some instructions under it, if you aren't a "figure it out" kind of person. If you have any ideas for improvement, please don't hesitate to share them with me!

Make sure you have the latest Flash player installed.

Click and drag on the circle to move it around the window.

Use the "SHOW" boxes at the top to choose what information to make visible.

Click on a quadrant in the toolbar to zoom in on that quadrant.

Use the zoom buttons to shrink and enlarge the circle.

The RESET button will put everything back the way it was when you started.

Click on one of the points on the circle to toggle the information that is shown.

HOW TO PRACTICE

TO LEARN RADIANS: Hide radian measures by clicking the box next to RADIANS. Work your way around the circle figuring out the radians. Click each point as you go to see if you are right.

TO LEARN COORDINATES: Hide coordinates by clicking the box next to COORD. Work your way around the circle figuring out the coordinates. Click each point as you go to see if you are right.

TO LEARN IT ALL: Turn off all four "SHOW" boxes then zoom in on a quadrant. Quiz yourself as to the information for a given point, then click the point to see if you are correct. Move on to another quadrant as you master the previous one.

REMEMBER: The unit circle is all about symmetry. Don't think of each point as its own disjoint item. Once you know the first couple points in the first quadrant, you know the entire circle. Use the symmetry to your advantage.

SUGGESTION:

It helps many people to count off in increments when deciding on radian measures of angles. For instance, starting at 0 radians and working counter-clockwise, and skipping 45 degree (π/4 radian) angles, you can say to yourself:

"zero, one π over six, two π over six, three π over six, four π over six, five π over six, six π over six, seven π over six, eight π over six, nine π over six, ten π over six, eleven π over six, and twelve π over six"

. . . then just simplify the fractions

repeat for the "45's"

"zero, one π over four, two π over four, three π over four, four π over four, five π over four, six π over four, seven π over four, eight π over four"

. . . and simplify those fractions (note you will have already found some of those the previous time around)

NEW FEATURES in Version 1.1

Version 1.1 now offers keyboard support and a "Quiz Me" feature!

Keyboard shortcuts:

+ zooms in

- zooms out

1, 2, 3, 4 choose the related quadrant

r resets the circle

q enables the "Quiz Me" feature

ENTER shows the answer while using the "Quiz Me" feature

"Quiz Me" feature:

Click the "Quiz Me" button in the toolbar (or press "q" on the keyboard) and a point will randomly be chosen on the unit circle.

To show the answer click the chosen point (or press ENTER on the keyboard).

Repeat the process as many times as you'd like.

To leave the "Quiz Me" feature, click RESET (or press "r" on the keyboard).

NEW FEATURES in Version 1.2

Version 1.2 now offers sound!

Sound is enabled by default. You will hear little clicks and bleeps as you use the application.

To turn sound off, click the speaker icon (or press "s" on the keyboard).