The cycloid is a transcendental plane curve defined by a point on a circle that rotates on a straight line without slipping.

The parametric equations for a cycloid are:

\(x=r \left( t-\sin t \right)\)

\(y=r \left( 1-\cos t \right)\)

where \(r\) is the radius of the circle.

In the applet below, click in the

**Start**button to begin the animation that shows the drawing of a cycloid. You can use the**Stop**button to stop the animation at any point. Click in the**Reset**button to erase the last curve. You can change the values of r in the slider in order to obtain different kinds of cycloids. You can also hide the circle and the half-line in order to see only the curve.
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