Generate random points on the perimeter of a circle

Question

I have a circle of radius r and access to a random number generator. What is a method to generate random (x,y) values distributed along the circle's perimeter?

Answer 1

The simplest method would be to generate a random angle $\theta \in [0,2\pi]$. Then convert from polar to Cartesian with $(x,y) = (r \cos \theta , r \sin \theta)$.

Note that if your random number generator returns a number $k \in [0,1]$ then $\theta = 2\pi k$.