Sine and cosine functions.

The sine and cosine function are very closely related and can be made equivalent simply by adjusting their initial phase:

$\displaystyle \sin\theta = \cos(\theta - \frac{\pi}{2})$ or $\displaystyle \qquad \cos\theta = \sin(\theta + \frac{\pi}{2}).$

Figure 5: Phase relationship between cosine (solid blue line) and sine (broked green line) functions.

$\scalebox{0.85}{\includegraphics{eps/plotcossin.eps}}$
In calculus, the sine and cosine functions are derivatives of one other. That is,

$\displaystyle \frac{d\sin\theta}{dt}=\cos\theta$ and $\displaystyle \qquad \frac{d\cos\theta}{dt}=-\sin\theta.$

**Figure 5:** Phase relationship between cosine (solid blue line) and sine (broked green line) functions.
$\scalebox{0.85}{\includegraphics{eps/plotcossin.eps}}$

``Music 270a: Sinusoids'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).