Sinus

$\displaystyle \sin^2 x$	$\displaystyle =$	$\displaystyle \frac{1}{2}\ \Big(1 - \cos (2x) \Big)$
$\displaystyle \sin^3 x$	$\displaystyle =$	$\displaystyle \frac{1}{4}\ \Big(3 \sin x - \sin (3x) \Big)$
$\displaystyle \sin^4 x$	$\displaystyle =$	$\displaystyle \frac{1}{8}\ \Big(\cos (4x) - 4 \cos (2x) + 3 \Big)$
$\displaystyle \sin^5 x$	$\displaystyle =$	$\displaystyle \frac{1}{16}\ \Big(10\, \sin x - 5 \sin (3x) + \sin (5x) \Big)$
$\displaystyle \sin^6 x$	$\displaystyle =$	$\displaystyle \frac{1}{32}\ \Big(10 - 15\, \cos (2x) + 6 \cos (4x) - \cos (6x) \Big)$
$\displaystyle \sin^n x$	$\displaystyle =$	$\displaystyle \frac{(-1)^{n/2}}{2^n}\ \sum_{k=0}^{n} (-1)^k {n \choose k} \cos\Big((n-2k)x \Big)\ ; \quad n \in \mathbb{N}$ und $\displaystyle n$ gerade
$\displaystyle \sin^n x$	$\displaystyle =$	$\displaystyle \frac{(-1)^{(n-1)/2}}{2^n}\ \sum_{k=0}^{n} (-1)^k {n \choose k} \sin \Big((n-2k)x \Big)\ ; \quad n \in \mathbb{N}$ und $\displaystyle n$ ungerade