Angular Frequency

Hey, I'm doing OCR A Level Physics, this question relates to module G484...

What is exactly meant by the angular frequency, in terms of simple harmonic motion?
On a question this came up and all was required to answer was 'the product of 2pi multiplied by the frequency.

Definition of frequency; number of oscillations per unit time.

There are 2 pi radians in a circle. I understand circular motion and simple harmonic motion are closely related. Are there 2 pi radians in one oscillation of simple harmonic motion? If this is correct this would help settle my query. If this is not the case why is angular frequency used for simple harmonic motion?
I have also read that angular frequency is the rate of change of phase?


Would this definition of angular frequency be correct and suffice....?

Rate of change of the angle subtended, measured in radians per second. w=2(pi)f

OR

'A measure of the frequency of an object varying sinusoidally, equal to 2pi multiplied by the frequency, expressed in radians per second'

Thanks for any help