How do you prove 1 radian is equal to 360 degree?

By definition, the number of radians in one complete revolution is given by the ratio of the circumference of a circle to its radius.

The circumference of a circle of radius r is of length 2πr.

There are thus 2πr/r = 2π radians in one revolution.

So, 2π radians = 360°

Then 1 radian = 360/2π = 57.296° or 57° 17'