I'm struggling with this problem, I'm still only on part (a). I tried X=rcos(theta) Y=rsin(theta) but I don't think I'm doing it right.
Curve C has polar equation r=sin(${\theta}$)+cos(${\theta}$).
(a) Write parametric equations for the curve C.
$\left\{\begin{matrix} x= \\ y= \end{matrix}\right.$
(b) Find the slope of the tangent line to C at its point where ${\theta}$ = $\frac{\pi}{2}$.
(c) Calculate the length of the arc for 0 $\leq {\theta} \leq {\pi}$ of that same curve C with polar equation r=sin(${\theta}$)+cos(${\theta}$).