how do i can solve a trigonometric equation which is restricted arguments?

#1 Posted: 2021/7/4 23:50:31

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Hi
i want to solve an equation about adding three cosine term which are constrained:

cos(2 pi(x+y-2z))+cos(2 pi(y+z-2x))+cos(2 pi(z+x-2y))=0

with constraint 0
can some one please guide me?

i wrote this command but it did not work:

solve({cos(2*Pi*(x+y-2*z))+cos(2*Pi*(y+z-2*x))+cos(2*Pi*(z+x-2*y)) = 0, 0 <= x, x <= 1, y <= 1, z <= 1, x < y, y < z}, [x, y, z], explicit)
when we write this command as this:
solve({cos(2*Pi*(x+y-2*z))+cos(2*Pi*(y+z-2*x))+cos(2*Pi*(z+x-2*y)) = 0,[x, y, z], explicit)
i do not see any change in the figures
apparently my restriction do not work!
whats the problem?
someone told me i should solve this problem with Draghilev method because this problem should solve with numerical method

#2 Posted: 2021/7/5 10:41:14

overlord

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More experienced users may help you better than me.
But your equation seems to have infinite solutions.

Regards

al_nleqsolve equ(x,y,z).sm (10.75 KiB) downloaded 599 time(s).

#3 Posted: 2021/7/5 18:20:46

Alvaro

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As overlord points, there are infinite solutions. Just like the better visual representation for z = f(x,y) is a surface in the 3D space, w = f(x,y,z) is a hypersurface in the 4D space. But we can't see that plot. So, here a plot of families of that 4D hypersurface, like a contour plot, but with surfaces.

About Dragilev method, I can't find my setup for 3D, and the expert there is Viacheslav (uni).

Plots4D.sm (111.28 KiB) downloaded 667 time(s).
Plots4D.pdf (393.96 KiB) downloaded 389 time(s).

Best regards.
Alvaro.

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Oscar Campo 2021/7/5 21:01:00

#4 Posted: 2021/7/5 21:15:59

Jean Giraud

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#5 Posted: 2021/7/6 01:46:40

Fridel Selitsky

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One of the solutions by the Draghilev method.

Draghilev.sm (23.95 KiB) downloaded 606 time(s).

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Alvaro 2021/7/6 03:06:00

#6 Posted: 2021/7/6 03:05:22

Alvaro

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Well, Fridel it's an expert too, thanks.

Joining above Dragilev and 4D methods.

Plots4D_DM3.sm (111.83 KiB) downloaded 647 time(s).
Plots4D_DM3.pdf (182.28 KiB) downloaded 362 time(s).

Best regards.
Alvaro.

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Fridel Selitsky 2021/7/6 03:50:00

#7 Posted: 2021/7/6 12:19:07

Fridel Selitsky

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Discussion of this problem on the maple forum featuring
the author of this question(rahmati)
https://www.mapleprimes.com/questions/232488-How-Do-I-Can-Solve-A-Trigonometric-Equation

SMath

how do i can solve a trigonometric equation which is restricted arguments?

how do i can solve a trigonometric equation which is restricted arguments? - maple software - Messages

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how do i can solve a trigonometric equation which is restricted arguments? - maple software - Messages