# Homework Help: Find exact solution for few angles!

1. Jun 10, 2012

### 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.

2. Jun 10, 2012

### 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)

3. Jun 10, 2012

### 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?

4. Jun 11, 2012

### 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.