Sinusoids

``Sinusoids'' may be represented using both sine and cosine functions having the form:

$\displaystyle \textcolor{blue}{ x(t) = A\sin(\omega t + \phi) \quad \mbox{\textcolor{black}{or}} \quad x(t) = A\cos(\omega t + \phi), }$

where

is the quantity that varies over time and

$\displaystyle A$	$\displaystyle \triangleq$	peak amplitude
$\displaystyle \omega$	$\displaystyle \triangleq$	radian frequency (rad/sec) $\displaystyle = 2\pi f$
$\displaystyle f$	$\displaystyle \triangleq$	frequency (Hz)
$\displaystyle t$	$\displaystyle \triangleq$	time (seconds)
$\displaystyle \phi$	$\displaystyle \triangleq$	initial phase (radians)

**Figure 1:** Sinusoid where , $\omega = 2\pi 5$ , and $\phi = \pi /4$ .
$\scalebox{0.8}{\includegraphics{eps/plotsin.eps}}$

``Music 171: Sinusoids'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).