Hello, gryphon5!
If I have a circle that is centered at (200,200) and its radius is 150,
how do I calculate the point at any given angle? Code:
 * * *
 * * P
 * *
 * r / *
 / 
 * / θ  *
 * O*    + *
 * (h,k) Q *

 * *
 * *
 * *
 * * *

 +               

Consider a circle with radius $\displaystyle r$ with center $\displaystyle O(h,k)$.
Point $\displaystyle P$ creates $\displaystyle \angle POQ$ with the horizontal.
In right triangle $\displaystyle PQO$, we have:
. . $\displaystyle \cos\theta = \frac{OQ}{r}\quad\Rightarrow\quad OQ = r\cos\theta$
. . $\displaystyle \sin\theta = \frac{PQ}{r}\quad\Rightarrow\quad PQ = r\sin\theta$
The $\displaystyle x$coordinate of $\displaystyle P$ is: .$\displaystyle x \:=\:h + OQ\:=\:h + r\cos\theta$
The $\displaystyle y$coordinate of $\displaystyle P$ is: .$\displaystyle y \:=\:k + PQ \:=\:k + r\sin\theta$
Therefore, point $\displaystyle P$ is at: .$\displaystyle \left(h + r\cos\theta,\:k + r\sin\theta\right) $