Differences
This shows you the differences between two versions of the page.
|
cosine_function [2014/01/29 19:51] nikolaj |
cosine_function [2014/03/21 11:11] |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ===== Cosine function ===== | ||
| - | ==== Function ==== | ||
| - | | @#FFBB00: $\mathrm{\cos}: \mathbb C\to\mathbb C$ | | ||
| - | | @#FFBB00: $\cos(z) := \sum_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}z^{2n} $ | | ||
| - | ==== Discussion ==== | ||
| - | $\theta\in\mathbb R$ | ||
| - | |||
| - | ^ $\cos(\theta) = \frac{1}{2}(\mathrm e^{i\theta}+\mathrm e^{-i\theta}) $ ^ | ||
| - | |||
| - | i.e. if $\zeta_\theta:=\mathrm e^{i\theta}$, then $\zeta_\theta+\overline{\zeta_\theta}=2\cos(\theta)$. | ||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Infinite sum of complex numbers]], | ||
| - | [[Factorial function]] | ||
| - | === Related === | ||
| - | [[Exponential function]], [[Sine function]] | ||
