The general form of a sinusoidal function is \(\displaystyle y(t) = A \sin (\omega t + \phi)\), where $\omega $ is the angular velocity of the function in radians/second and $\phi$ is the phase angle, which is essentially the offset of the function. You can think of \(\displaystyle \phi\) as shifting the sine wave to the left or the right, but it has no effect on the "speed" with which the sine wave moves up and down.

The period for the sinusoidal function is \(\displaystyle \frac {2 \pi} {\omega}\), and the frequency in hertz (cycles per second) is \(\displaystyle f = \frac 1 T = \frac {\omega} {2 \pi}\)$.