Sine

trigonometry

Definition

Sine

The trigonometric function $\sin (z)$ ($z\in \mathbb{C}$) can be defined as power series:

$$\sin (z):=\sum _{n=0}^{\infty }(-1{)}^n\frac{z^{2n+1}}{(2n+1)!}$$

Additivity Theorem

Let $x,y\in \mathbb{R}$, then it holds that:

$$\sin (x+y)=\sin x\cdot \cos y+\sin y\cdot \cos x$$