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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!

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    In what sense is this "a Cartesian equation of a cycloid"? Assuming that $c$ is a constant, it's just an equation for $x$ which, depending on the function $a(x)$, can have any number of solutions for $x$; how does that describe a cycloid?2011-08-18
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    @joriki: Indeed, thanks for the valid point. What if I let $a(x) = k\sqrt{y(x)}$ where $k$ is a constant? I shall edit the post.2011-08-18
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    @joriki: Ignore the sqrt... I really meant let $a(x) = ky(x)$...2011-08-18
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    It really can't be a cycloid; you have a $y$ outside your square root in the implicit Cartesian equation...2011-08-18
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    I have edited the question by throwing in some square roots, is this a cycloid now?2011-08-18
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    @jake: Frankly, I've lost interest. You just changed the question for the third time. Why do you think someone should spend time on this version if they can expect it to change a few more times? If you want people to spend time to help you, you should be more careful with their time.2011-08-18

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