A curve in polar coordinates is given by: $r = 8 + 4 \cos \theta.$
Point $P$ is at $\theta = \frac{20 \pi}{16}.$

a.) Find polar coordinate $r$ for $P$, with $r \gt 0$ and $\pi \lt \theta \lt \frac{3 \pi}{2} .$
$r =$

b.) Find cartesian coordinates for point $P.$
$x =$
$y =$

c.) How may times does the curve pass through the origin when $0 \lt \theta \lt 2 \pi ?$
Answer: