Definition:Sine/Real Function

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

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

Graph of Sine Function


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.