Recall, the equations for a cycloid from a circle with radius are: Suppose we make our circle larger. For example, let . How do we need to adjust our equations? The correct curve is shown in blue. Adjust the values for , , and to fix the pink curve to match. Change the radius to using the slider. Adjust , , and again to make the curve match.

## Parametric Equations for Cycloid

The equations for a cycloid created by a circle with radius rolling on the -axis are: ______ ______