I'm trying to derive the basic form of a sine wave:
$$y = A \cdot \sin(\omega t + \theta)$$
I'm guessing I could probably first derive the cosine wave as follows and then add a phase of $-\frac{\pi}{2}$.
$$y = Re(z) = Re(A \cdot \cos(\omega t) + i\cdot \sin(\omega t)) = A \cdot \cos(\omega t)$$
Is this derivation the most common method and if it isn't what are other ways could I use to derive the basic form of a sine wave? Any other info regarding this basic form would be greatly appreciated as well?
Hint:
simply you have:
$$ y=A\sin(\omega t +\theta)=A\cos (\omega t +\theta -\dfrac{\pi}{2}) $$
So the two forms represents the same function an can be derived the one by the other simply by a change of $\theta$.