I have completed a GeoGebraBook of nine Unit Circle Symmetry applets, which you can use by clicking here. There are three applets per type of symmetry on the unit circle, one focusing on the unit circle only, and the other two linking unit circle properties to patterns in the graphs of the sine and cosine functions.

When two angle expressions, such as and , exhibit symmetry on the unit circle, mastery of unit circle symmetries and reference angles often allow function arguments to be simplified. Mastery of symmetries and reference angles will also be very handy when expanding inverse trigonometric function results to describe all possible answers to a problem.

Suggestions for improvements to these applets, or additional applets, are always welcome via comments on this post.