Convert $x(t)$ and $y(t)$ into Cartesian form Consider the parametric equations given by \begin{align*} x(t)&=\sin{t}-t,\\ y(t) & =  1-\cos{t}.\end{align*}
I want to write these parametric equations in Cartesian form. 
In order to eliminate the sine and cosine terms I think I probably need to consider some combination of $x(t),y(t), x(t)^2$ and $y(t)^2$ but I can't see exactly how to do this. 

From the second equality, you'll get $t=\arccos(1-y)$. So,\begin{align}x&=\sin\bigl(\arccos(1-y)\bigr)-\arccos(1-y)\\&=\sqrt{1-(1-y)^2}-\arccos(1-y)\\&=\sqrt{2y-y^2}-\arccos(1-y).\end{align}
