Maclaurinsche Reihe: Sinus
1. Satz
\begin{align*}
\sin(x) =& x - \frac{1}{3!} x^3 + \frac{1}{5!}x^5 - \frac{1}{7!}x! ...
\end{align*}
2. Beweis
\begin{align*}
\sin(x) =& 0 + x + \frac{0}{2!} x^2 + \frac{-1}{3!} x^3 + \frac{0}{4!} x^4 + \frac{1}{5!}x^5 + ... \\
=& x - \frac{1}{3!} x^3 + \frac{1}{5!}x^5 - \frac{1}{7!}x!
\end{align*}