# Definition:Sine/Real Function

## Definition

The real function $\sin: \R \to \R$ is defined as:

 $\ds \forall x \in \R: \,$ $\ds \sin x$ $=$ $\ds \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {x^{2 n + 1} } {\paren {2 n + 1}!}$ $\ds$ $=$ $\ds x - \frac {x^3} {3!} + \frac {x^5} {5!} - \cdots$

### Arch of Sine Function

Each section of the sine function between adjacent zeroes is called an arch of the sine function

## Also see

• Results about the sine function can be found here.