We have that

1 Radian = $\displaystyle \frac{180}{\pi}$ degrees

Then isn't it true that

$\displaystyle \frac{1}{1}=1$ Radians = $\displaystyle \frac{\pi}{180}$ degrees?

Also, I was reading in a precalc book that the area of a sector of a circle is $\displaystyle \frac{1}{2} \times r^2 \times \theta$, where $\displaystyle \theta$ is the angle in radians. As I'm not used to using radians, I usually do $\displaystyle \frac{r^2 \times \pi \times \Phi}{360}$ where $\displaystyle \Phi$ is the angle in degrees. Can someone please explain slowly how to transfer from one to the other?