Period

One cycle of a sinusoid is $2\pi$ radians.

Figure 6: Sinusoid.

Since sinusoids are periodic with period $2\pi$, an initial phase of $\phi$ is indistinguishable from an initial phase of $\phi \pm 2\pi$. We may therefore restrict the range of $\phi$ so that it does not exceed $2\pi$. Typically we choose the range

$$-\pi < \phi < \pi,$$

but we many also encounter

$$0 < \phi < 2\pi.$$

The period $T$ of a sinusoid is the time (in seconds) it takes to complete one cycle.