I have a prolate cycloid: $$\begin{align*} x &= 2 - \pi\cos(t)\\ y &= 2t - \pi\sin(t) \end{align*}$$ over the interval $-\pi \leq t \leq \pi$, crossed itself at point $P$ on the $x$-axis
a) Find the equations of the 2 tangent lines at $P$
b) find the points on curve where tangent line is horizontal.
c) find the point on curve where tangent line is vertical.
So I know for part $b$ and $c$, you just need to use the derivatives $dx$ and $dy$ and then solve for when $dx=0$ and $dy=0$... however for part a), do I just simply take the derivative of both $x$ and $y$ and that is my solution?