I've been battling with parametric equations recently and one of the situations I came across was a system of parametric equations that graph the cycloid of circle with radius $a$, which looks as follows:
$y=a(1-\cos\theta)$, $x=a(\theta-\sin\theta)$
Now I'm aware that it's possible to remove the parameter in this system (the parameter being either a or $\theta$), but is it possible to remove both? And also, when expressing $\theta$ in terms of x, is this process correct:
$\frac{x}{a}=\theta-\sin\theta$
$\sin^{-1}(\frac{x}{a}) = 2\theta$
$\frac{\sin^{-1}(\frac{x}{a})}{2}=\theta$