Editing Sine wave (section)

{{Short description|Wave shaped like the sine function}}
{{redirect-distinguish|Sinusoid|Sinusoid (blood vessel)}}
{{onesource|date=January 2024}}
[[File:One positive frequency component, cosine and sine, from rotating vector (fast animation).gif|class=skin-invert-image|thumb|282x282px|Tracing the y component of a [[circle]] while going around the circle results in a sine wave (red). Tracing the x component results in a [[cosine]] wave (blue). Both waves are sinusoids of the same frequency but different phases.]]

A '''sine wave''', '''sinusoidal wave''', or '''sinusoid''' (symbol: '''∿''') is a [[periodic function|periodic wave]] whose [[waveform]] (shape) is the [[trigonometric function|trigonometric]] [[sine|sine function]]. In [[mechanics]], as a linear [[motion]] over time, this is ''[[simple harmonic motion]]''; as [[rotation]], it corresponds to ''[[uniform circular motion]]''. Sine waves occur often in [[physics]], including [[wind wave]]s, [[sound]] waves, and [[light]] waves, such as [[monochromatic radiation]]. In [[engineering]], [[signal processing]], and [[mathematics]], [[Fourier analysis]] decomposes general functions into a sum of sine waves of various frequencies, relative phases, and magnitudes.

When any two sine waves of the same [[frequency]] (but arbitrary [[phase (waves)|phase]]) are [[linear combination|linearly combined]], the result is another sine wave of the same frequency; this property is unique among periodic waves. Conversely, if some phase is chosen as a zero reference, a sine wave of arbitrary phase can be written as the linear combination of two sine waves with phases of zero and a quarter cycle, the ''sine'' and ''cosine'' [[vector component|components]], respectively.