# [Maxima] A Question about a trigonometric identity

Richard Hennessy rich.hennessy at verizon.net
Mon Nov 16 17:17:29 CST 2009

```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