'elliptical' trigonometric functions

A point moves with constant angular velocity on an ellipse. Drag the gold dots to choose an ellipse. Click on the icon in the lower left hand corner of either panel to see an animation. What curves are traced out in he left hand panel? Why do they look like that? How do the curves in the left hand panel vary when you rotate the ellipse in the right hand panel? Explain why they behave as they do.