===== Cosine function =====
==== Function ====
| @#FFBB00: definiendum | @#FFBB00: $\mathrm{\cos}: \mathbb C\to\mathbb C$ |
| @#FFBB00: definiendum | @#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 $\zeta:=\mathrm e^{i\theta}$, then $\zeta+\overline{\zeta}=2\cos(\theta)$.
==== Parents ====
=== Context ===
[[Infinite sum of complex numbers]], 
[[Factorial function]]
=== Related ===
[[Exponential function]], [[Sine function]]