sine of an angle in degree mode

[rflesch]

On the classic HP calculators, in degree mode, sin(180) is exactly equal to zero, and I don't understand why:
(a) angles are internally represented in units of radians as far as I know;
(b) the sine function is a transcendental function; whatever algorithm is used, it cannot give us the exact result in a finite number of steps.
Both (a) and (b) should lead to a small deviation from zero.