[scythe]

CORDIC is not based on radians or turns; it is based on decomposing the angle into a sum of:

phi_n = atan(2^-n)

and then using an abbreviated sum formula where computing cos(theta + phi_n) depends only on sums and bitshifts.

The small-angle approximations sin(x) ≈ x and cos(x) ≈ 1-x^2/2 are the real killer feature of radians, though, because when you can deal with the loss of accuracy you get to avoid using any loops whatsoever. They're also fundamental to understanding simple physical systems like a pendulum.