# Sinusoid

(redirected from*sinusoidally*)

Also found in: Dictionary, Thesaurus, Medical, Wikipedia.

## sinusoid

[′sī·nə‚sȯid]## Sinusoid

(or sine curve), the graph of the function *y* = sin *x*. It is a plane curve (see Figure 1) representing the variation in the sine as the argument, or angle, changes. A sinusoid intersects the *x*-axis at the points 180°*k* (or *πk*) and has maxima at the points 90° + 360°*k* (or *π/2 + 2- πk) and minima at the points - 90° + 360°k (or - π/2* + 2

*πk*), where

*k*= 0, ± 1.....

The curve defined by the equation *y* = *A* sin (*ωx* + Φ_{0}) is also sometimes called a sinusoid. The relation between this curve and the curve *y =* sin *x* is as follows: first, the *x*-coordinates of the points of *y* = sin *x* are increased by a factor of *ω*; second, the *y*-coordinates of the points of *y* = sin *x* are increased by a factor of *A;* and third, the curve is translated by an amount - Φ_{0}/*ω* along the *x*-axis. The number *A* is called the amplitude, *ω* is called the angular frequency, and Φ/_{0} is called the initial phase angle. The sinusoid is of great importance in the theory of oscillations. [23–1296–]