How do I calculate a point on a circle’s circumference?

The parametric equation for a circle is

x = cx + r * cos(a)
y = cy + r * sin(a)

Where r is the radius, cx,cy the origin, and a the angle.

That's pretty easy to adapt into any language with basic trig functions. Note that most languages will use radians for the angle in trig functions, so rather than cycling through 0..360 degrees, you're cycling through 0..2PI radians.

Here is my implementation in C#:

    public static PointF PointOnCircle(float radius, float angleInDegrees, PointF origin)
    {
        // Convert from degrees to radians via multiplication by PI/180        
        float x = (float)(radius * Math.Cos(angleInDegrees * Math.PI / 180F)) + origin.X;
        float y = (float)(radius * Math.Sin(angleInDegrees * Math.PI / 180F)) + origin.Y;

        return new PointF(x, y);
    }

Who needs trig when you have complex numbers:

#include <complex.h>
#include <math.h>

#define PI      3.14159265358979323846

typedef complex double Point;

Point point_on_circle ( double radius, double angle_in_degrees, Point centre )
{
    return centre + radius * cexp ( PI * I * ( angle_in_degrees  / 180.0 ) );
}