Edited...
I have a Cartesian equation of a cycloid: $$\arcsin\left(k\sqrt{y(x)}\right) - k\sqrt{y(x)-k^2y(x)^2} + c = x$$ where $k$ and $c$ are constants.
How might I parameterize it so that I get the usual parameterizations, i.e. $$\begin{align*} x&=r(t-\sin{t})\\ y&=r(1-\cos{t}) \end{align*}$$?
Thanks in advance!