$(50$ Points$)$ For the following polar functions:

First: sketching the graph of $r$ as a function of $$ in Cartesian coordinates, Then: sketch the polar curve.

$($a$)r=1+2cos$

$($b$)r={}^2$ for $-22$

$($c$)r=2sin6$

$($d$)r=sin(\frac{}{2})$

$($e$)r=cos(\frac{}{3})$