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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: how to solve trigonometric equation
Date: Wed, 8 Jun 2011 02:20:06 +0000 (UTC)
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"Philippe " <philippeb3@hotmail.com> wrote in message <ismjm4$qe6$1@newscl01ah.mathworks.com>...
> Dear all,
> 
> I would like to solve the following equation between 0 and 2 pi.
> 
> A*sin(w*t-p)+2*B*sin(2*w*t-q)=0
> 
> where A, B, w, p, q are constants.
> 
> t=?
> 
> Is there any way in Matlab to solve this equation?

You can do it by hand. Start with the sin of a sum
identity to get rid of those p and q terms.

sin(x+y) = ...

Then reduce sin(2*x) using a similar identity.

In the end, you reduce this to a polynomial in
sin(w*t). Solve for the roots of that polynomial.
Once you know all possible solutions, then
compute t using an asin.

You do the work though, not me.

John