Definition:Sine Curve

Definition
A sine curve is the graph of a real function which can be expressed in the form:
 * $\forall x \in \R: \map f x = a \map \sin {m x + \epsilon}$

where $a$, $m$ and $\epsilon$ are arbitrary constants.

It is usual to suppose that:
 * $a$ and $m$ are non-zero

and either:
 * $0 \le \epsilon \le 2 \pi$

or:
 * $-\pi \le \epsilon \le \pi$