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In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...
The characteristic wave patterns of periodic functions are useful for modeling recurring phenomena such as sound or light waves. [28] Under rather general conditions, a periodic function f (x) can be expressed as a sum of sine waves or cosine waves in a Fourier series. [29]
Sine or cosine waves that make up the original function will appear as peaks in the frequency domain functions produced by the sine or cosine transform, respectively. The Fourier sine transform of f ( t ) {\displaystyle f(t)} is: [ note 1 ]
A triangle wave with period p and amplitude a can be expressed in terms of sine and arcsine (whose value ranges from −π/2 to π/2): = ( ()). The identity = can be used to convert from a triangle "sine" wave to a triangular "cosine" wave.
Polarization (waves) Coherence (physics), the quality of a wave to display a well defined phase relationship in different regions of its domain of definition; Hilbert transform, a method of changing phase by 90° Reflection phase shift, a phase change that happens when a wave is reflected off of a boundary from fast medium to slow medium
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 wave whose waveform (shape) is the trigonometric sine ...
The typical convention of using the cosine phase instead of the sine phase when describing a wave is based on the fact that the cosine is the real part of the complex exponential in the wave A e i ( k x − ω t ) . {\displaystyle Ae^{i\left(kx-\omega t\right)}.}
The cosine function and all of its Taylor polynomials are even functions. In mathematics , an even function is a real function such that f ( − x ) = f ( x ) {\displaystyle f(-x)=f(x)} for every x {\displaystyle x} in its domain .