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:

$-\pi \le \epsilon \le \pi$

Also see

• Results about sine curves can be found here.

Linguistic Note

The adjective used to describe a sine curve is sinusoidal.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): sine curve
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): sine curve
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): sine curve