# [Maxima] How to simplifiy a*sin(x)+b*cos(x)

Richard Hennessy rvh2007 at comcast.net
Sat Sep 6 10:50:25 CDT 2008

```"And a useful transformation."  I agree, it gives some insight into Fourier Series.

Rich

------------Original Message------------
From: "Stavros Macrakis" <macrakis at alum.mit.edu>
To: fateman at cs.berkeley.edu
Cc: "Maxima List" <maxima at math.utexas.edu>
Date: Fri, Sep-5-2008 12:46 PM
Subject: Re: [Maxima] How to simplifiy a*sin(x)+b*cos(x)
On Fri, Sep 5, 2008 at 12:14 PM, Richard Fateman <fateman at cs.berkeley.edu> wrote:

try expand(trigsimp(trigexpand(    sqrt(b^2+a^2)*sin(x+atan(b/a))  )));
but that is in the reverse direction.

This proves the equality, but as you say doesn't perform the transformation the user wants to perform.

Your notion of simplification is more like complification.

No, it is more like "transformation" to another form.  And a useful transformation.  I can't think of a straightforward way to perform this transformation in general in Maxima; I don't think the pattern matcher is powerful enough to find the appropriate subexpression of, e.g.

a*sin(q)+b*cos(r)+c*cos(q)

without explicitly being told it is looking for terms in sin/cos(q).

-s

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