Solving a symbolic system of equations

I'm trying to solve a symbolic system of equations in MATLAB, but it keeps giving me zero for the variables I'm solving for. I know this isn't the answer since I worked the problem out by hand. Is there a way to use the solve function to do this?

% Equillateral Strain Rosette Problem

% angle values (A = 0, B = 120; C =60; seems to be standard for a 60 degree
% equilateral triangle)
A = 0;
B = 120;
C = 60;
% Given Angles
ThetaA = deg2rad(A); %radians for A, it always seems to start at 0
ThetaB = deg2rad(B); %in an equillateral triangle seems to be 180-interior angle
ThetaC = deg2rad(C); %seems to be just interior angle

syms strainx strainy strainxy strainA strainB strainC
strainA = (strainx+strainy)/2 + (strainx-strainy)/2*cos(2*ThetaA) + strainxy*sin(2*ThetaA);
strainB = (strainx+strainy)/2 + (strainx-strainy)/2*cos(2*ThetaB) + strainxy*sin(2*ThetaB);
strainC = (strainx+strainy)/2 + (strainx-strainy)/2*cos(2*ThetaC) + strainxy*sin(2*ThetaC);

eqns = [strainA, strainB, strainC];
vars = [strainx, strainy, strainxy];
[strainx, strainy, strainxy] = solve(eqns,vars); %Need to solve in terms of strainA strainB and strainC

Answer 1

[Stephan]

Try:

% Equillateral Strain Rosette Problem

% angle values (A = 0, B = 120; C =60; seems to be standard for a 60 degree
% equilateral triangle)
A = 0;
B = 120;
C = 60;
% Given Angles
ThetaA = deg2rad(A); %radians for A, it always seems to start at 0
ThetaB = deg2rad(B); %in an equillateral triangle seems to be 180-interior angle
ThetaC = deg2rad(C); %seems to be just interior angle

syms strainx strainy strainxy strainA strainB strainC
eq(1) = strainA == (strainx+strainy)/2 + (strainx-strainy)/2*cos(2*ThetaA) + strainxy*sin(2*ThetaA);
eq(2) = strainB == (strainx+strainy)/2 + (strainx-strainy)/2*cos(2*ThetaB) + strainxy*sin(2*ThetaB);
eq(3) = strainC == (strainx+strainy)/2 + (strainx-strainy)/2*cos(2*ThetaC) + strainxy*sin(2*ThetaC);

vars = [strainx, strainy, strainxy];
[strainx, strainy, strainxy] = solve(eq,vars) %Need to solve in terms of strainA strainB and strainC

which gives:

strainx =
 
strainA
 
 
strainy =
 
(2*strainB)/3 - strainA/3 + (2*strainC)/3
 
 
strainxy =
 
-(3^(1/2)*(strainB - strainC))/3