Sine: Expansions
Series:

sin(x) =
(-1)^{k} x^{2k+1} / (2k+1)!

= x - (1/3!)x^{3} + (1/5!)x^{5} - (1/7!)x^{7}

(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})*...