Subject: problem solving multiple trigonometric equations
From: Barton Willis
Date: Tue, 22 Jun 2010 16:38:17 -0500
-----maxima-bounces at math.utexas.edu wrote: -----
>Very?recently?I?started?using?Maxima?and?already?got?some?usefull?results.
>However,?I?now?stumbled?on?a?problem?with?solving?mutliple?equations
>involving
>trigonometric?functions.?A?simple?(not?very?usefull)?example:
>
>(%i1)?solve([cos(x)?=?1/2,?sin(y)?=?1/2],?[x,y]);
>(%o1)?????????????????????????????????[]
Maxima has two alternative solve functions. I know little about one
of these, but the optional package to_poly_solver can solve trigonometric
equations that can be converted into polynomial equations that algsys can solve.
Try this:
(%i1) load(to_poly_solver)$
(%i8) %solve([cos(x) = 1/2, sin(y) = 1/2], [x,y], 'simpfuncs = ['ratexpand]);
(%o8) %union([x=2*%pi*%z58-%pi/3,y=2*%pi*%z58+(5*%pi)/6],[x=2*%pi*%z60-%pi/3,y=2*%pi*%z60+%pi/6],[x=2*%pi*%z62+%pi/3,y=2*%pi*%z62+(5*%pi)/6],[x=2*%pi*%z64+%pi/3,y=2*%pi*%z64+%pi/6])
The user documentation for to_poly_solve is
.../maxima/share/contrib/topoly-user-doc.html
where ... depends on the location of your Maxima. Welcome to Maxima.
Let us know if you have questions about to_poly_solver or Maxima in
general.
--Barton