I'm reading Higher Math for Beginners by Zeldovich and Yaglom and exercise 1.8.5 states:
Express the parametric dependence $$x = r (t—sin (t)), y = r (1 — cos (t))$$ explicitly, in the form of a function $x= φ (y)$
I've been working on this all afternoon but all i seem to run into are dead ends
I've only gotten as far as expressing $t = cos^{-1}( \frac{r - y }{r}$) but after that no matter how much i try to square, transpose and substitute the initial equations i always seem to reach a dead end. The answer according to the book is:
$x = rcos^{-1}( \frac{r - y }{r}) - \sqrt{2ry-y^2}$
The answer looks like it's in the form of the first equation but that hasn't seemed to help.