# Sinusoid

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## sinusoid

[′sī·nə‚sȯid]
(anatomy)
Any of the relatively large spaces comprising part of the venous circulation in certain organs, such as the liver.
(mathematics)

## 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 + 2πk), where k = 0, ± 1.....

Figure 1

The curve defined by the equation y = A sin (ωx + Φ0) 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 - Φ0/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–]

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