Animation of sine and cosine on the unit circle + the graphs of sine and cosine are waves!

The cosine function is just the x coordinate of a point moving along the unit circle, and the sine function is just the y coordinate of a point moving along the unit circle. So we can show an animation of sine and cosine on the unit circle by highlighting the components of the radius as our point revolves around the unit circle.

At the same time, we show animations of the graphs of sine and cosine as our point revolves around the unit circle and the sine and cosine components grow and shrink accordingly. After a couple periods it becomes clear why sines and cosines are the basis for the mathematics of waves: the graphs of sine and cosine are waves!