```Path: news.mathworks.com!not-for-mail
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)
Organization: John D'Errico (1-3LEW5R)
Lines: 28
Message-ID: <ismm8l\$3bt\$1@newscl01ah.mathworks.com>
References: <ismjm4\$qe6\$1@newscl01ah.mathworks.com>
NNTP-Posting-Host: www-01-blr.mathworks.com
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-Trace: newscl01ah.mathworks.com 1307499606 3453 172.30.248.46 (8 Jun 2011 02:20:06 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Wed, 8 Jun 2011 02:20:06 +0000 (UTC)
Xref: news.mathworks.com comp.soft-sys.matlab:730735

"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
```