A curtate cycloid is the curve traced by a point at a distance
h
from the center of a circle of radius
R
rolling along the
x
-axis, where
x=R\theta -hsin(\theta ),y=R-hcos(\theta )hh. Show that the curtate
cycloid has parametric equations x=R\theta -hsin(\theta ),y=R-hcos(\theta ). See the
figure below (the distance between the red and black dots is h ):