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 cosine_function [2014/01/29 19:51]nikolaj cosine_function [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2014/01/29 19:51 nikolaj 2014/01/29 19:51 nikolaj 2014/01/29 19:49 nikolaj 2014/01/29 19:49 nikolaj 2014/01/29 19:48 nikolaj 2014/01/29 19:48 nikolaj 2014/01/29 19:47 nikolaj 2014/01/29 19:47 nikolaj 2014/01/29 19:44 nikolaj 2014/01/29 19:33 nikolaj created Next revision Previous revision 2014/01/29 19:51 nikolaj 2014/01/29 19:51 nikolaj 2014/01/29 19:49 nikolaj 2014/01/29 19:49 nikolaj 2014/01/29 19:48 nikolaj 2014/01/29 19:48 nikolaj 2014/01/29 19:47 nikolaj 2014/01/29 19:47 nikolaj 2014/01/29 19:44 nikolaj 2014/01/29 19:33 nikolaj created Line 1: Line 1: ===== Cosine function ===== ===== Cosine function ===== ==== Function ==== ==== Function ==== - | @#FFBB00: $\mathrm{\cos}:​ \mathbb C\to\mathbb C$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\mathrm{\cos}:​ \mathbb C\to\mathbb C$ | - | @#FFBB00: $\cos(z) := \sum_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}z^{2n}$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\cos(z) := \sum_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}z^{2n}$ | ==== Discussion ==== ==== Discussion ==== Line 9: Line 9: ^ $\cos(\theta) = \frac{1}{2}(\mathrm e^{i\theta}+\mathrm e^{-i\theta})$ ^ ^ $\cos(\theta) = \frac{1}{2}(\mathrm e^{i\theta}+\mathrm e^{-i\theta})$ ^ - i.e. if $\zeta_\theta:=\mathrm e^{i\theta}$,​ then $\zeta_\theta+\overline{\zeta_\theta}=2\cos(\theta)$. + i.e. if $\zeta:=\mathrm e^{i\theta}$,​ then $\zeta+\overline{\zeta}=2\cos(\theta)$. ==== Parents ==== ==== Parents ==== - === Requirements ​=== + === Context ​=== [[Infinite sum of complex numbers]], ​ [[Infinite sum of complex numbers]], ​ [[Factorial function]] [[Factorial function]] === Related === === Related === [[Exponential function]], [[Sine function]] [[Exponential function]], [[Sine function]]