> [!NOTE] Definition (Sine & Cosine) > For $x\in\mathbb{R}$ we define the *trigonometric functions* by the [[Power Series|power series]] $\begin{align} \cos(x) &= \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{2n}}{(2n)!} \\ \sin(x) &= \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{2n+1}}{(2n+1)!} \end{align}$