Question

How to mathematically divide a circle into 60 parts with coordinates?

Answer 1

The coordinates are (rcos(6n),rsin(6n)) where r is the radius of the circle and n ranges from 0 to 59.
60 parts gives the angle 360/60=6 degrees, so multiples of this angle (6n) determine the coordinates.
When n=0, the coords are (r,0); when n=5, the coords are (r√3/2,r/2); when n=10 the coords are (r/2,r√3/2), etc.