I'm trying to convert the parametric equation $x = \cos (t) ; y = \sin (t)-t^2$ to rectangular form but have gotten stuck trying to eliminate the last $t$ from parametric form. I have gotten as far as: $y = \sqrt(1-x^2) - \arccos(x)^2$.
I know that $t = \arccos(x)$ but I have no idea how to square that quantity.
It becomes more complicated:
$x=\cos t ⇒ t= Arc\ cos x $
$\sin t = \sqrt{1 - x^2}$
$y^2/25=sin^2 t - (32/5)t^2 \sin t+(256/25) t^4$
$x^2+y^2/25= cos^2t+ sin^2t - (32/5)t^2 \sin t+(256/25) t^4$
$x^2+y^2/25=1-(32/5)(Arc \cos x)^2 \sqrt{1-x^2}+(256/25)(Arc\cos x)^4$