I have the general parametric equation of an ellipse.
$\begin{align*}x&=c_x+a\cos{t}\cos{\alpha}-b\sin{t}\sin{\alpha} \\ y&=c_y+a\cos{t}\sin{\alpha}+b\sin{t}\cos{\alpha}\end{align*}$
I need to find the value of $t$ when $x$ and $y$ are known. I tried solving the equation and ended up with
$t = \arccos{\frac{(x-c_x)\cos{\alpha} + (y-c_y)\sin{\alpha}}{a}}$
The first thing that bothers me about this equation is that it doesn't depend on $b$. The major issue is, it seems that the value of $t$ I get is more and more inaccurate with increasing $\alpha$.
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