sinusoid

A sine wave or sine wave is a type of plane curve describing a uniform oscillation. It is named after the sine function, whose graph is also a sine wave, as is the graph of the cosine function. The sinusoid is often found in physics, where it is used to describe oscillatory movements, and in a number of other applications. A general sinusoid as a function of time t has Eq

A graph of two sinusoids of the same frequency and amplitude, but different phases{\displaystyle y(t)=A\sin(2\pi ft+\varphi )=A\sin(\omega t+\varphi ),}

where

A is referred to as the amplitude (the maximum value reached by the sinusoid)
f is the frequency (the number of oscillations per unit time, usually per second)
{\displaystyle \varphi }is the phase, given in radians, and expresses the position of the cycle at time t = 0
{\displaystyle \omega }= 2π f is the angular frequency, expressing the rate of oscillation in radians per second
The importance of the sinusoid also stems from the fact that the sum of two sinusoids of the same frequency again gives a sinusoid of this frequency, regardless of the amplitudes and phases of the summaries. Other types of waves do not have this property, and it gives the sinusoid a privileged role in the field of harmonic analysis of signals.