Maclaurin Series for Sine and Cosine

Q1: What is the Maclaurin series for cosx?
A1: $cosx=1-\frac{x^2}{2}+\frac{x^4}{4!}-\frac{x^6}{6!}+...$
$cosx=\sum\limits_{n=0}^\infty \frac{(-1)^nx^n}{2n!}$

Q2: What is the Maclaurin series for sinx?
A2: $sinx=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...$
$sinx=\sum\limits_{n=0}^\infty \frac{(-1)^nx^n}{(2n+1)!}$