trigonometric equations



Maxima has at least two alternative solve functions. I don't know much
about the
function "Solver", but I wrote to_poly_solve. Neither of these alternative
solve
functions can do what you want:

 (%i11) load(to_poly_solver)$
 (%i14) load(solver)$

 (%i12) algexact : true$
 (%i23) to_poly_solve(cos(2*x) =1/2 - sin(x),x);

OK, but too complicated:

 (%o23) %union([x=2*%pi*%z82+atan((2^(3/2)*(sqrt(5)/4-1/4))/sqrt(sqrt
 (5)+5))-%pi],[x=2*%pi*%z84-atan((2^(3/2)*(sqrt(5)/4-1/4))/sqrt(sqrt
 (5)+5))],  [x=2*%pi*%z86-atan((2^(3/2)*(sqrt(5)/4+1/4))/sqrt(5-sqrt
 (5)))+%pi],[x=2*%pi*%z88+atan((2^(3/2)*(sqrt(5)/4+1/4))/sqrt(5-sqrt(5)))])

As far as I know, Solver doesn't handle this equation:

 (%i24) Solver([cos(2*x) =1/2 - sin(x)],[x]);
 (%o24) [[[(2*cos(2*x)+2*sin(x)-1)/2]]]


Barton

-----maxima-bounces at math.utexas.edu wrote: -----

>To:?<maxima at math.utexas.edu>
>From:?"Jos?Simons"?<simons17 at xs4all.nl>
>Sent?by:?maxima-bounces at math.utexas.edu
>Date:?10/08/2009?08:54AM
>Subject:?[Maxima]?trigonometric?equations
>
>
>
>
>
>
>
>L.S.,
>
>How?can?I?solve?with?Maxima?the?equation
>
>
>cos(2*x)?=1/2?-?sin(x)
>
>in?such?a?way?that?I?get?the?exact
>solutions
>3/10?pi,?7/10?pi,?11/10?pi,?19/10?pi,
>etc.
>
>Thanking?you?in?advance?for?your
>answer.
>
>Regards,
>
>Jos??Simons
>?_______________________________________________
>Maxima?mailing?list
>Maxima at math.utexas.edu
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