Definition:Sine/Analysis

Definition

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

$\displaystyle \sin x = \sum_{n=0}^\infty \left({-1}\right)^n \frac {x^{2n+1}}{\left({2n+1}\right)!} = x - \frac {x^3} {3!} + \frac {x^5} {5!} - \cdots$

Sources

• Murray R. Spiegel: Mathematical Handbook of Formulas and Tables (1968): $20.21$
• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 16.2$