Solve equation with 2 unknowns using solve

How to solve the two equation below?

cos(3a)+cos(3b)=0
cos(a)+cos(b)=1.6

Ans:

a = 7.6 degree = 0.132645 rad

b = 52.4 degree = 0.9145525 rad

Hereby my code

syms a b
sol = solve(cos(3*a)+cos(3*b)==0, cos(a)+cos(b)==1.6,[a,b])
sol.a
sol.b

and it gave me this

In sym/solve>warnIfParams (line 478)

In sym/solve (line 357)

sol =

struct with fields:

a: [1×1 sym]

b: [1×1 sym]

ans =

z

ans =

z1

Answer 1

[Walter Roberson]

syms a b
sol = vpasolve(cos(3*a)+cos(3*b)==0, cos(a)+cos(b)==1.6,[a,b],[0, pi; 0, pi])

sol = struct with fields:
    a: [1×1 sym]
    b: [1×1 sym]

sol.a

ans = 

0.91660896848843414923150917923804

sol.b

ans = 

0.13058858270816359692270528185513

Your equations are symmetric in your variables, so this is an equivalent solution to what you posted.

[Jane Low]

Thank you :)

Answer 2

[Alan Stevens]

There are an infinite number of solutions! Restrict the range. One possibility is as follows

bfn = @(a) acos(1.6-cos(a));
fn = @(a) cos(3*a)+cos(3*bfn(a));

a0 = 0.1;  % initial guess
a = fzero(fn, a0);
b = bfn(a);

disp([a, b])

    0.1306    0.9166

disp(rad2deg([a,b]))

    7.4822   52.5178

[Jane Low]

Thank you :)