Maclaurinsche Reihe: Cosinus
1. Satz
\begin{align*}
\cos(x) =& 1 - \frac{1}{2!} x^2 + \frac{1}{4!}x^4 - \frac{1}{6!}x^6 + \frac{1}{8!}x^8 ...
\end{align*}
2. Herleitung
\begin{align*}
\cos(x) =& 1 + \frac{0}{1!}x + \frac{-1}{2!}x^2 + \frac{0}{3!}x^3 + \frac{1}{4!}x^4 ... \\
=& 1 - \frac{1}{2!} x^2 + \frac{1}{4!}x^4 - \frac{1}{6!}x^6 + \frac{1}{8!}x^8 ...
\end{align*}