Answer
The parametric equations of the curtate cycloid is
$c(t)=(R{\ } t-h \sin t,R-h \cos t)$.
Work Step by Step
Let P be the point on the cycloid at time $t$. For the circle of radius R its circumference is $2{\ }\pi{\ }R$, so at time $t$ the circle has moved $R{\ }t$ distance to the right of the $y$-axis. From the figure, we see that the coordinates of P is
$x=R{\ }t-h\cos (t-\pi/2)=R{\ }t-h \sin t$
$y=R+h \sin (t-\pi/2)=R-h \cos t$
Hence, the parametric equations of the curtate cycloid is
$c(t)=(R{\ }t-h \sin t,R-h \cos t)$.
