# [Maxima] A Question about a trigonometric identity

Stavros Macrakis macrakis at alum.mit.edu
Mon Nov 16 18:04:11 CST 2009

```Yes, but as far as I know there is no easy way in Maxima to convert in this
direction:

a*sin(x)+b*cos(x) => q*sin(x+r)

The other direction is of course trivial -- expand(trigexpand(...))

-s

On Mon, Nov 16, 2009 at 6:17 PM, Richard Hennessy <rich.hennessy at verizon.net
> wrote:

> a*sin(b)+c*cos(b) is always a phase shift with a possible amplitude change
> as well.
>
> Rich
>
>
> ----- Original Message -----
> From: "Martin Mallinson" <Martin at mallinson.homeip.net>
> To: <maxima at math.utexas.edu>
> Sent: Monday, November 16, 2009 1:35 PM
> Subject: [Maxima] A Question about a trigonometric identity
>
>
> >I am new to Maxima, never having used this mailing list before, and I
> > wonder
> > if anyone can help clarify this small problem I have?.
> >
> > eq1: R = (3^(3/2)*sin(z)-3*cos(z))/4;
> > trigrat(%);
> > print("Maxima fails to simplify the expression. But...");
> > subst(z1+%pi*2/3,z,eq1);
> > trigrat(%);
> > subst(z-%pi*2/3,z1,%);
> > print("Maxima now shows us that eq1 was in fact just a phase shift");
> > print("How can I get Maxima to show this without the two subst
> > operations?");
> >
> > My problem of course, is that I had to guess that the expression was a
> > simple
> > phase shift, had I not guessed this, I would never have got there...
> >
> > Thanks for any help
> > Martin M
> >
> > By the way - thank you all for supporting Maxima. I had the pleasure of
> > working with Macsyma on the Symbolic XL1200 -- I have the original
> > Symbolics Macsyma documentation someplace. It is wonderful to have
> > access to Maxima as an open source project. Thank you.
> >
> >
> > _______________________________________________
> > Maxima mailing list
> > Maxima at math.utexas.edu
> > http://www.math.utexas.edu/mailman/listinfo/maxima
> >
>
>
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