sine of an angle in degree mode

[Werner]

SIN(180°) is zero because that is the exact result - contrary to Pi, 180 is exactly representable, and so an exact result can be given.
SIN and COS in degrees are first reduced to the interval 0°-45° before converting to radians, which can be done without introducing errors (the reduction I mean), meaning SIN(180°) is reduced to SIN(0°) = 0.
SIN(Pi) is also zero, and for CAS-enabled calculators that is the result given. In dealing with real numbers, Pi is no longer exactly representable, but is rather rounded to the calculator's precision, and you calculate
SIN(3.14159265359), which is NOT SIN(Pi). And since SIN(Pi - x) = SIN(x) ~= x for very small x, that is what you get.

Cheers, Werner