Every once in a while I try to create something that just acts as a"tug" to get the user moving in the direction of dynamic math. Here is a little file that just demonstrates something that a lot of teachers might never think of because without dynamic geometry it is massively ugly.
It just involves controlling the rates at which two points travel on an ellipse, and tracks the midpoint of the segment connecting them. Many PreCalculus books include sections on polar graphs, based heavily on trig. This takes those shapes and modifies them. A sketch based on circles can be found here.
If you would like to play around with this file, get it now!