sine of an angle in degree mode

[rflesch]

Thomas Okken wrote:
"If PI SIN returns 0, you're either using CAS or the internal version of pi has the same number of digits as the PI function on the keyboard.

— I don't understand the second part of this sentence. If the internal representation of pi has the same number of digits as as the PI function on the keyboard then I would get zero as a result of SIN PI??

On the 15C, "PI SIN" gives "-4.1E-10" (indicating the CORDIC algorithm with 10 digits is used).
Aren't there two sources of error in the result that's displayed:
(a) the finite number of digits of the internal representation of pi;
(b) the approximative character of the algorithm?
So I would think that "-4.1E-10" is not exactly the sine of the internal representation of pi in the calculator.