Vector Valued Function Problem

If someone could help me with this problem, I would greatly appreciate the help. I believe I have the solution to the first part, but I'm not sure about the second part.

"Show that one arch of the cycloid r(t) = <t-sint, 1-cost> has length 8. Find the value of t in [0,2PI] where the speed is at a maximum"

Thanks!

Same answer, corrected procedure

Oops. Right you are, UCSociallyDead. Got ahead of myself.

$\displaystyle speed=s(t)=|r'(t)|=\sqrt{2-2\cos t}$

So $\displaystyle acceleration=s'(t)=(2-2\cos t)^{-1/2}\sin t=0$

So $\displaystyle t=0$ or $\displaystyle t=\pi$, but if $\displaystyle t=0$, you have a zero in the denominator, which doesn't work. Therefore, the only stationary point occurs at $\displaystyle t=\pi$. I'll let you have the pleasure of taking another derivative to prove it's a max, not a min. (Hi)