How to find the coordinates of a regular polygon on a circle given the number of sides of the polygon, the radius, and the coordinates of one point.

Question

I need to write a program that calculates the points of the corners of a regular polygon on a circle. I don't need programming help, just the math. I know that one point will always be at the "3 O'Clock position." I'm also given the radius and number of sides of the polygon. How can I find the other points of the polygon (all sides are the same length) on the bounding circle?

Below is an image of an example.

Example of a 5 sided polygon:

Answer 1

For radius $r$ and $n$ sides you need the points to have coordinates $$(\cos \frac{2\pi t }{n},\sin \frac{2\pi t }{n})$$ for $t=0,1,2, ..., n-1$.