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Solve equation with 2 unknowns using solve

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Jane Low
Jane Low on 30 Jun 2021
Commented: Jane Low on 30 Jun 2021
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

Accepted Answer

Walter Roberson
Walter Roberson on 30 Jun 2021
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.

More Answers (1)

Alan Stevens
Alan Stevens on 30 Jun 2021
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

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