Recall, the equations for a cycloid from a circle with radius [math]r=1[/math] are:[br][math]x_t=-\sin t+t[/math][br][math]y_t=-\cos t+1[/math][br]Suppose we make our circle larger. For example, let [math]r=3[/math]. How do we need to adjust our equations?[br][math]x_t=-a\sin t+bt[/math][br][math]y_t=-a\cos t+c[/math][br]The correct curve is shown in blue. Adjust the values for [math]a[/math], [math]b[/math], and [math]c[/math] to fix the pink curve to match.[br][br]Change the radius to [math]r=5[/math] using the slider. Adjust [math]a[/math], [math]b[/math], and [math]c[/math] again to make the curve match.
The equations for a [b]cycloid[/b] created by a circle with radius [math]r[/math] rolling on the [math]x[/math]-axis are:[br][math]x_t=-[/math]___[math]\sin t+[/math]___[math]t[/math][br][math]y_t=-[/math]___[math]\cos t+[/math]___
[br][math]x_t=-r\sin t+rt[/math][br][math]y_t=-r\cos t+r[/math]