Editing Phase (waves) (section)

==Formula for phase of an oscillation or a periodic signal==
The phase of a [[Simple harmonic motion|simple harmonic oscillation]] or [[sine|sinusoidal signal]] is the value of <math display=inline>\varphi</math> in the following functions:
<math display="block">\begin{align}
  x(t) &= A\cos( 2 \pi f t + \varphi ) \\
  y(t) &= A\sin( 2 \pi f t + \varphi ) = A\cos\left( 2 \pi f t + \varphi - \tfrac{\pi}{2}\right)
\end{align}</math>
where <math display="inline"> A</math>, <math display="inline"> f</math>, and <math display="inline"> \varphi</math> are constant parameters called the ''amplitude'', ''frequency'', and ''phase'' of the sinusoid.  These signals are periodic with period <math display="inline"> T = \frac{1}{f}</math>, and they are identical except for a displacement of <math display="inline"> \frac{T}{4}</math> along the <math display="inline"> t</math> axis.  The term ''phase'' can refer to several different things:
* It can refer to a specified reference, such as <math display="inline"> \cos(2 \pi f t)</math>, in which case we would say the ''phase'' of <math display="inline"> x(t)</math> is <math display="inline"> \varphi</math>, and the ''phase'' of <math display="inline"> y(t)</math> is <math display="inline"> \varphi - \frac{\pi}{2}</math>.
* It can refer to <math display="inline"> \varphi</math>, in which case we would say <math display="inline"> x(t)</math> and <math display="inline"> y(t)</math> have the same ''phase'' but are relative to their own specific references.
* In the context of communication waveforms, the time-variant angle <math display="inline"> 2 \pi f t + \varphi</math>, or its [[principal value]], is referred to as ''[[instantaneous phase]]'', often just ''phase''.