Convert Rectangular Equations to Polar

x=r\cdot cos\theta

y=r\cdot sin\theta

Example: x^{2}+(y-4)^{2}=16

(r\cdot cos\theta)^{2}+(r\cdot sin\theta -4)^{2}=16

r^{2}cos^{2}\theta+r^{2}sin^{2}\theta-8r\cdot sin\theta+16=16

r^{2}cos^{2}\theta+r^{2}sin^{2}\theta-8r\cdot sin\theta+16-16=16-16

r^{2}cos^{2}\theta+r^{2}sin^{2}\theta-8r\cdot sin\theta+8r\cdot sin\theta=0+8r\cdot sin\theta

r^{2}cos^{2}\theta+r^{2}sin^{2}\theta=8r\cdot sin\theta

r^{2}(cos^{2}\theta+sin^{2}\theta)=8r\cdot sin\theta

\frac{r^{2}(1)}{r}=\frac{8r\cdot sin\theta}{r}

r=8sin\theta