Dear colleagues,
Maxima is very powerful system and also usable in the school mathematics.
Sometimes the answers of CAS are different than we expect in the school.
Trigonometric equations could be quite complicated for manual solving and
also for computer algebra systems.
My questions is about the answers offered by Maxima.
It seems that the command "solve" solves only the simpler equations and
gives a particular solution, like
solve(sin(x)=1/2,x);
[x=%pi/6]
In case of a bit more complicated examples, arc sine is in the answer.
solve(sin(x)=1/3,x);
[x=asin(1/3)]
It seems that some equations are too complicated for "solve" command.
solve(sin(x)-sqrt(3)*cos(x)=0,x);
[sin(x)=sqrt(3)*cos(x)]
It is possible to load the package "to_poly_solver"
load("to_poly_solver");
Then
%solve(sin(x)=1/2,x);
%union([x=2*%pi*%z26+%pi/6],[x=2*%pi*%z28+(5*%pi)/6])
%solve(sin(x)=1/3,x);
%union([x=2*%pi*%z36+atan(1/2^(3/2))],[x=2*%pi*%z38-atan(1/2^(3/2))+%pi])
%solve(sin(x)-sqrt(3)*cos(x)=0,x);
%union([x=2*%pi*%z6-(2*%pi)/3],[x=-(-4*%pi*%z8-(2*%pi)/3)/2])
There are the general solutions but maybe always not in the best form.
My question is about the borders - when command "solve" works and when
does not.
Is the to_poly_solver %solve the best way to solve trigonometric equations
in Maxima?
What about the solving strategies of the trigonometric equations?
Is it any documentation about solving trigonometric equations in
Maxima available?
Thank you very much!
Eno