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The graph of the function (see Fig.). The sinusoid is a continuous curve with period . It intersects the -axis at the points . These are also points of inflection, meeting the -axis at an angle of . The extrema are at the points .

Figure: s085640a

The graph of is the cosinusoid, obtained by shifting the sinusoid a distance of to the left. The cosinusoid intersects the -axis at the points , and its extrema are at the points .

Many oscillatory processes can be described by a periodic function of the form , where , and are constants and . The graph of this function (called a general sinusoid) is obtained from the graph of (the ordinary sinusoid) as follows: expand in the direction of the -axis by a factor , contract in the -direction by a factor , translate to the left over a distance , and when : reflect in the -axis. Its period is and it meets the -axis at the points . Its extrema are at the points .


Comments

In this article, .

See also Sine; Trigonometric functions.

How to Cite This Entry:
Sinusoid. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Sinusoid&oldid=15670
This article was adapted from an original article by Yu.A. Gor'kov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article