Sine: Expansions

Series:
sin(x) = (-1)^k x^2k+1 / (2k+1)!
= x - (1/3!)x³ + (1/5!)x⁵ - (1/7!)x⁷
(This can be derived from Taylor's Theorem.)

Product:
sin(x) = x (1 - (x / kPI)²)
= x(1 - (x/PI)²)(1 - (x/2PI)²)(1 - (x/3PI)²)*...