Sine and Cosine: 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**.)

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

= 1 - (1/2!)x^{2} + (1/4!)x^{4} - (1/6!)x^{6}

(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})*...