'Circling' the Square

Topic:
Functions
What kinds of trigonometric functions are generated by traversing the periphery of a square rather than a circle? What are the analogs of sine and cosine? What identities do these functions satisfy? You can animate the movement of the point by clicking on the symbol in the lower left hand corner of either window. You can move the point along the periphery by dragging the small dot on the head of the arrow.