How can i change this code????

syms w phi k
eq1 = cos(phi)*cos(k)==-0.340110;
eq2 = -cos(phi)*sin(k)==0.999407;
eq3 = sin(phi)==0.004822;
eq4 = cos(w)*sin(k)+sin(w)*sin(phi)*cos(k)==-0.999419;
eq5 = cos(w)*cos(k)-sin(w)*sin(phi)*sin(k)==-0.034096;
eq6 = -sin(w)*cos(phi)==0.000621;
eq7 = sin(w)*sin(k)-cos(w)*sin(phi)*cos(k)==0.000784;
eq8 = sin(w)*cos(k)+cos(w)*sin(phi)*sin(k)==-0.004798;
eq9 = cos(w)*cos(phi)==0.999988;
[w phi k] = solve(eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9)

I want to get w, phi and k

What's wrong...?

[Ameer Hamza]

You have 9 equations and only three variables. This system of equation is overdetermined. The answer shows that their is nor solution which can make the nine equations true.

Answer 1

[David Goodmanson]

Hi KK,

yes, nine equations, three unknowns. However,

[1] from eqn3 you can find phi. There are two solutions for phi, one close to zero and the other slightly less than 180. For the first solution cos(phi) is positve and for the second solution cos(phi) is negative, Assume the first solution, which puts you in the first quadrant.

[2] From eqn1 and eqn2 you can calculate k using atan2. The solution will be in the third quadrant since both sin(k) and cos(k) are negative.

[3] From eqn6 and eqn9 you can calculate w using atan2. The solution will be in the fourth quadrant since sin(w) is negative and cos(w) is positive.

The four remaining equations can be used as consistency checks.

For the second solution, phi --> 180 - phi; cos(phi) --> -cos(phi) sin(phi) same

k --> k + 180 [or k - 180] cos(k) --> -cos(k) sin(k) --> -sin(k)

w --> w + 180 [or w - 180] cos(w) --> -cos(w) sin(w) --> -sin(w)

If sin(phi) stays positive and all the other trig functions change sign, then all nine equations are unaffected as you can check.