Question

How do computers evaluate trigonometric functions like cos and sin?

Answer 1

\begin{align}
cos(x) = 1-\frac{x^2}{2!}&+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}-\frac{x^{10}}{10!}\\\\
&+\frac{x^{12}}{12!}-\frac{x^{14}}{14!}+\frac{x^{16}}{16!}-\frac{x^{18}}{18!}+...
\end{align}

Answer 2

cos and sin can be approximated to any degree of accuracy by a taylor series

Answer 3

if we can construct a polynomial to "fit" the curve, it makes life somewhat easier to deal with. Since derivatives tell us how a curve moves, a taylor series adds up all the subsequant derivatives so that they match the desired curve at a given point.