## There's no Trig Identity for this is there?

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Strill
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### There's no Trig Identity for this is there?

For a wave described by:
A*sin(x)+B*sin(x-PI/3)

I'd like to describe it in terms of a single sine or cosine function.

It does reduces to A * sqrt(3) *sin(x-PI/6), but only if A=B

I can't seem to find any identity that would work if A is not equal to B though. Am I right in assuming that it's not possible to describe this wave in terms of a single sine or cosine function when A is not equal to B?

stapel_eliz
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For a wave described by: A*sin(x)+B*sin(x-PI/3)

I'd like to describe it in terms of a single sine or cosine function.
Is this the sort of thing you're looking for?
More generally, for an arbitrary phase shift, we have

$a\sin x+b\sin(x+\alpha)= c \sin(x+\beta)\,$

where

$c = \sqrt{a^2 + b^2 + 2ab\cos \alpha},\,$

and

$\beta = \arctan \left(\frac{b\sin \alpha}{a + b\cos \alpha}\right) + \begin{cases} 0 & \text{if } a + b\cos \alpha \ge 0, \\ \pi & \text{if } a + b\cos \alpha < 0. \end{cases}$

Strill
Posts: 2
Joined: Mon Oct 17, 2011 10:33 pm
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### Re: There's no Trig Identity for this is there?

Yes, thank you that's exactly what I was looking for.