How to solve nonlinear Trigonometry equations in matlab
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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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Accepted Answer
Star Strider
on 5 May 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 Comments
Lonny Thompson
on 22 Jun 2020
yes, you need optimization toolbox to use fsolve.
another way to solve is using the symbolic toolbox solve function.
Star Strider
on 22 Jun 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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