I got a non-answer from solve()

Here's some code. I know that one solution is eta = pi/6, A=20, and k=2*pi/lambda. I get a non-answer (A=A, eta=eta, k=k) from solve():

reset(symengine);clear all;
syms x lambda A k positive;
syms eta;

lambda = 1;
eq1 = A*sin(eta)-10;
eq2 = A*sin(k*lambda/6 + eta)-20;
eq3 = A*sin(k*5*lambda/12 + eta);

% try to solve
solve(eq1,eq2,eq3,A,eta,k)

ans = 

        A: [1x1 sym]
      eta: [1x1 sym]
        k: [1x1 sym]

Other things I've tried have yielded different results, but they were also non-productive. What am I missing here?

Thanks,

Susan

Answer 1

[Sean de Wolski]

You get an answer!

b = solve(eq1,eq2,eq3,A,eta,k)

b.A  %A
b.eta  %eta
b.k    %k

[Susan]

I got a return value, but not a solution.

[Susan]

Oh, I get it now. ans.A is a double. Thanks

[Sean de Wolski]

I get numerical answers:

>> b.A

ans =

-42.761798705987901549528556940761

>> b.eta

ans =

125.42766685085308712979111364121653

>> b.k

ans =

-14.513150434658265763705596183829

[Sean de Wolski]

ans.A is a sym, convert it to double with double

double(ans.A);

[Walter Roberson]

Those values for A and k are incompatible with the "syms A k positive" that Susan had.

[Sean de Wolski]

I just copied and pasted what she had...

Answer 2

[Walter Roberson]

Sometimes instead of putting an assumption on the range of a variable, it is better to select() the answers that meet the criteria.

[Walter Roberson]

By selecting the admissible solutions after finding them all, the complete set I get is

[A = 20, eta = (1/6)*Pi, k = 2*Pi]

[A = 20, eta = (5/6)*Pi, k = 10*Pi]

[A = (80/7)*14^(1/2), eta = -arctan((1/11)*7^(1/2))+Pi, k = -12*arctan(7^(1/2))+12*Pi]

[A = (80/7)*14^(1/2), eta = arctan((1/11)*7^(1/2)), k = 12*arctan(7^(1/2))]}