I recently did an angular velocity problem where they gave the angular velocity (rate of rotation) and asked me to write it as a cosine function of the form:

f(x) = a * cos [k (x - d)] + c

A tutor told me that "k", the constant of horizontal compression, is also the angular velocity, so that:

Period = (2pi) / abs(k)

This means that the sinusoidal function is related to a circle and can be used to model angular velocity.

Is there some theorem that relates the sinusoidal function to the unit circle? I am interested in knowing about this, and google returned nothing relevant. I would appreciate some further research into this.