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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?

FisherDisinformation
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Tarius
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    What does it mean to "derive the form of a sine wave"? In particular, derive from what? – David C. Ullrich Jun 19 '15 at 20:19
  • $\sin()$ and $\cos()$ are equally fundamental. There's no advantage in deriving $\sin()$ from $\cos()$ over $\cos()$ from $\sin()$, unless you just have an assignment where you are told to do that. If you understand the relationship between them, you're already there. – bob.sacamento Jun 19 '15 at 20:25

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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 $\theta$.

Emilio Novati
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