Math2.org Math Tables:

Sine and Cosine
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Sine and Cosine: 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.)

cos(x) = (-1)^k x^2k / (2k)!
= 1 - (1/2!)x² + (1/4!)x⁴ - (1/6!)x⁶
(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)*...