Cosine series and sine series/R/Definition

Sine (series)

For ${}x\in \mathbb {R}$, the series

$\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n}}{(2n)!}}$

is called the cosine series, and the series

$\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n+1}}{(2n+1)!}}$

is called the sine series in ${}x$.