Parameterizing a curve 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!

I don't think this is a cycloid, at least not a full cycloid up to a cusp. The cusp of a cycloid has infinite curvature. This curve has finite curvature everywhere.
