Hi, I am having trouble reversing the formula [tex] x=R(\theta - \sin(\theta))[/tex] to get [tex]\theta[/tex] in terms of x. Am I missing something obvious or is it just impossible?(adsbygoogle = window.adsbygoogle || []).push({});

To put it into context this is part of the parametric equation for a cycloid. The other part of the parametric equation is [tex] y = R (1- \cos(\theta))[/tex]. Setting R to 1 (the radius of the rolling wheel) does not seem to help. The non parametric equation for the cycloid is [tex] \pm \cos^{-1}((R-y)/R) \pm \sqrt{2 R y -y^2}[/tex]. I would also like to reverse this full equation to get y in terms of x but I am having trouble with that too. The reason I am trying to reverse the equations is that I am trying to get the intersection of two loci (the cycloid locus and the perimeter of a ellipse).

Any help appreciated. Thanks :)

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# Parametric equation for a cycloid

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