Find exact solution for few angles

[abotaha]

Hi everybody,

I have a couple of equations and I need to find the values of three variables (δ, λ, and θ).
The equations are:

M[11] = -(sin(δ)*cos(λ)*sin(2*θ)+sin(2*δ)*sin(λ)*sin(θ)^2)*M[0];
M[12] = (sin(δ)*cos(λ)*cos(2θ)+(1/2)*sin(2*δ)*sin(λ)*sin(2θ))*M[0];
M[13] = -(cos(δ)*cos(λ)*cos(θ)+cos(2*δ)*sin(λ)*sin(θ))*M[0];
M[22] = (sin(δ)*cos(λ)*sin(2*θ)-sin(2*δ)*sin(λ)*cos(θ)^2)*M[0];
M[23] = -(cos(δ)*cos(λ)*sin(θ)-cos(2*δ)*sin(λ)*cos(θ))*M[0];
M[33] = sin(2*δ)*sin(λ)*M[0];

where :
M[0]= 19.817; M[11]= 32.6; M[12] = -1.3; M[13] = -7.2; M[22] = 2.2; M23 = -13.5; M[33] = -24.7;

Any help would be highly appreciated.

 

[drszdrsz]

The last one:

This is straightforward to show that there's no exist δ λ such that:

-24.7= sin(2*δ)*sin(λ)*19.817

(this can be true only if δ λ are complex)

 

[christoff]

I have to agree with drszdrsz; some of these equations will not have real solutions. In particular, the first and last do not have real solutions.

As for the other ones... do it numerically?

 

[abotaha]

Thanks for the replay. I also tried to solve these equations and i found that the solution contained complex number, however, the solution suppose to be real number.
i do not know how i can processed further.
please i need some suggestions.

 

[Levex]

Complex numbers might reduce to real numbers if you properly transform your equations...