How to solve nonlinear Trigonometry equations in matlab

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

Answer 1

[Star Strider]

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

[Mohsen]

Thank you very much!

[Star Strider]

My pleasure!

[Mahroo Sajid]

Hi,

Do I need to install a toolbox for using this method? I am getting an error when I try this.

[Lonny Thompson]

yes, you need optimization toolbox to use fsolve.

another way to solve is using the symbolic toolbox solve function.

[Star Strider]

Another option is to use fminsearch:

[B,fv] = fminsearch(@(b)norm(f(b)-0), B0)

It may not be as accurate, however it will provide decent parameter estimates.

.