How to solve nonlinear Trigonometry equations in matlab
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Mohsen
el 5 de Mayo de 2015
Comentada: Star Strider
el 22 de Jun. de 2020
Dear Friend I have a 5 nonlinear trigonometry equations with 5 parameters as following:
x*sin(z)-y*sin(k)=-2.061 ,
y*cos(k)-x*cos(z)=5.181 ,
x*cos(0.4904-z)+0.1*y*cos(0.4904+z)=0 ,
-1.032*cos(u)-0.1*y*sin(k)-0.2*x*sin(z)=-0.8821 ,
-1.032*sin(u)+0.1*y*cos(k)+0.2*x*cos(z)=-0.471 ,
How to calculate x,y,z,k,u? Best Regards
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Respuesta aceptada
Star Strider
el 5 de Mayo de 2015
One possibility:
% MAPPING: b(1) = x, b(2) = y, b(3) = z, b(4) = k, b(5) = u
f = @(b) [b(1)*sin(b(3))-b(2)*sin(b(4))+2.061
b(2)*cos(b(4))-b(1)*cos(b(3))-5.181
b(1)*cos(0.4904-b(3))+0.1*b(2)*cos(0.4904+b(3))
-1.032*cos(b(5))-0.1*b(2)*sin(b(4))-0.2*b(1)*sin(b(3))+0.8821
-1.032*sin(b(5))+0.1*b(2)*cos(b(4))+0.2*b(1)*cos(b(3))+0.471];
B0 = rand(5,1)*2*pi;
[B,fv,xf,ops] = fsolve(f, B0);
ps = ['x'; 'y'; 'z'; 'k'; 'u'];
fprintf(1, '\n\tParameters:\n')
for k1 = 1:length(B)
fprintf(1, '\t\t%s = % .4f\n', ps(k1,:), B(k1))
end
that with one set of initial parameter estimates produces:
Parameters:
x = 0.9478
y = 5.8864
z = 1.6950
k = 0.5351
u = 1.1792
5 comentarios
Lonny Thompson
el 22 de Jun. de 2020
yes, you need optimization toolbox to use fsolve.
another way to solve is using the symbolic toolbox solve function.
Star Strider
el 22 de Jun. de 2020
[B,fv] = fminsearch(@(b)norm(f(b)-0), B0)
It may not be as accurate, however it will provide decent parameter estimates.
.
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