On 04/02/2010 06:18 PM, Enrico H?rtel wrote:
> Dear all,
>
> I am trying to solve the following equation using Maxima 5.20.1:
>
> solve (sin(x) = cos(x),x)
>
> The result shown is [sin(x) = cos(x)]
>
> I tried to figure out how get an explicit solution for x. There is a document
> [1] pretending that Maxima is not capable to do this. Are they right?
>
> Thank you in advance
> Enrico H?rtel
>
>
> [1] www.tex-sales.se/Artiklar/MaximaMuPAD.pdf, p24
>
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>
This is one of those things that maxima should be able to do, but
apparently cannot in the form which the problem is written.
Note:
(%i6) display2d: false;
(%o6) false
(%i7) solve(cos(x)^2=sin(x)^2,x);
(%o7) [sin(x) = -cos(x),sin(x) = cos(x)]
(%i8) solve(cos(x)^2=1-cos(x)^2,x);
solve: using arc-trig functions to get a solution.
Some solutions will be lost.
(%o8) [x = 3*Pi/4,x = Pi/4]
(%i9) solve(sqrt(1-x^2)=x,x);
(%o9) [x = sqrt(1-x^2)]
(%i10) solve(1-x^2=x^2,x);
(%o10) [x = -1/sqrt(2),x = 1/sqrt(2)]
(%i11) acos(1/sqrt(2));
(%o11) Pi/4
(%i12) acos(-1/sqrt(2));
(%o12) 3*Pi/4
I hope someone with enough knowledge will work on the trig equations to
add this kind of feature.
Clearly, one can solve any polynomial of degree less than five in
maxima, so, using acos(x), one should be able to solve any trigonometiic
equation p(cos(x))=0 where $p$ has degree less than 5.
FWIW
-sen