This dynamic diagram illustrates the three main trig functions -- sine, cosine and tangent -- along with their reciprocals -- cosecant, secant and cotangent. Note that the tangent and cotangent are actually lines tangent to the circle. The secant and cosecant cut through the curve, which is what secant lines do. And the sine and cosine -- well, those are based on mistranslations from Sanskrit through Arabic through Latin to English.
Grab the blue ring with your mouse (or finger, if you have a touch pad) and drag it around the circle. Observe how each of these elements waxes and wanes as the angle changes.

Trig Functions on the Unit Circle

Impress your friends with this printable diagram for your refrigerator.