The Purplemath Forums

by **Strill** on Mon Oct 17, 2011 10:39 pm

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?

**Sponsor**

by **stapel_eliz** on Tue Oct 18, 2011 1:12 am

Strill wrote: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? :wink:

Wikipedia wrote: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

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

by **Strill** on Tue Oct 18, 2011 6:19 pm

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

The Purplemath Forums

There's no Trig Identity for this is there?

There's no Trig Identity for this is there?

Re: There's no Trig Identity for this is there?