Cycle and (Initial) Phase

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

The phase refers to the position within the cycle and is dependent on whether using a

1. sine function ( $\sin(\omega t)$):
   
   
   
   

2. or a cosine function ( $\cos(\omega t)$):
   
   
   
   

The initial phase is the phase at time = 0 and is

$$\textcolor{blue}{ -\pi < \phi < \pi, } \quad \mbox{ \textcolor{black}{or} } \quad \textcolor{blue}{ 0 < \phi < 2\pi. }$$