No solution found when solving 3 non linear equations

Good day every one

I have been trying to sove 3 non linear equations but i am "No solution found" report.

The code is as follows

I defined a function containing the 3 non linear equations in an mfile called "angle"

function F=myfunction(x)

F(1)=cos(-x(1)+x(2))+cos(-x(1)+x(3));
F(2)=cos(-x(2)+x(1))+cos(-x(2)+x(3));
F(3)=cos(-x(3)+x(1))+cos(-x(3)+x(2)); 

After running code

deltarad=fsolve(@yyyyy,rand([3 1]))

I get the following report

No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
default value of the function tolerance.
<stopping criteria details>

deltarad =

  -60.5208
  -62.8602
  -61.6905


fsolve stopped because the sum of squared function values, r, has gradient with
relative norm 7.341307e-07; this is less than options.OptimalityTolerance = 1.000000e-06.
However, r = 7.954251e-01, exceeds sqrt(options.FunctionTolerance) = 1.000000e-03.

Optimization Metric                                          Options
norm(grad r) =   7.34e-07                        OptimalityTolerance =   1e-06 (default)
r =   7.95e-01                               sqrt(FunctionTolerance) =  1.0e-03 (default)

[Walter Roberson]

The equations are not consistent.

[Manqoba Mazibuko]

Thank you. Can you please advise of how check the consistency of these equations?

[Walter Roberson]

Solve any two of them for two of the variables. Substitute into the third. Observe that the result is something that cannot be 0.

[Manqoba Mazibuko]

Thank you I just did that. They are inconsistent. Thank you for the help, really appreciate it!!!

Answer 1

[Matt J]

A numerical sweep also gives evidence that there is no solution

[x1,x2,x3]=ndgrid(linspace(-pi,+pi,512));


F1=cos(-x1+x2)+cos(-x1+x3);
F2=cos(-x2+x1)+cos(-x2+x3);
F3=cos(-x3+x1)+cos(-x3+x2); 

F=[abs(F1(:)), abs(F2(:)), abs(F3(:))];

Fmin = min(sum(F,2))

Fmin =

    1.0142

Answer 2

[Alex Sha]

Hi, all, how about the solutions below, from the numerical perspective：

1：

x1: -5.21219473201765E21
x2: -0.279500437676178
x3: 1.29129588911872

Fevl:
f1=0
f2=-1.4930819167841E-15
f3=-1.4930819167841E-15

2:

x1: -1.79664678356017E21
x2: 2.02595283616513
x3: 3.59674916296003

Fevl:
f1=0
f2=-3.04739415125932E-15
f3=-3.04739415125932E-15

3:

x1: 2.19768008763813
x2: 5.41140930100612E22
x3: 0.626883760843237

Fevl:
f1=3.61394399649162E-15
f2=0
f3=3.61394399649162E-15

[Matt J]

I can't reproduce your f values

x1= -5.21219473201765E21
x2= -0.279500437676178
x3= 1.29129588911872

F1=cos(-x1+x2)+cos(-x1+x3)
F2=cos(-x2+x1)+cos(-x2+x3)
F3=cos(-x3+x1)+cos(-x3+x2)

F1 =

   -0.2352


F2 =

   -0.1176


F3 =

   -0.1176

[Walter Roberson]

With that range of values, some of your x are within eps() of the others and so the additions lose precision.