zero(s) of a nonlinear implicit function

I want to find the roots of an implicit function whose dependant variable is impossible to isolate. In particular, I want to find a array of outputs for a given array of inputs. That function is

1.5786+3*cosd(theta4-1.0714*cosd(theta2)-cosd(theta4-theta2)=0

Here, theta2 is the input and theta4 is the output. A function m-file:

function theta4 = fourbar(theta2)
theta2=0:0.5:360;
for i =1:length(theta2)
1.5786+3*cosd(theta4(i))-1.0714*cosd(theta2(i))-cosd(theta4(i)-theta2(i))
end

In the command prompt with an initial guess of 0.01 does not work:

fsolve(@fourbar,0.01)

How can I pass the elements of theta2 to the function 'fourbar' and then solve for theta4 in another array?

Answer 1

[Walter Roberson]

In particular, I want to find a array of outputs for a given array of inputs.

That is not possible using fsolve() -- not unless you use a for loop or arrayfun to process one at a time.

fsolve() is strictly for a single output given a vector of input parameters.

[Walter Roberson]

syms theta2 theta4 real
C1 = sym(1.0714);
eqn = sym(pi)/2+3*cosd(theta4)-C1*cosd(theta2)-cosd(theta4-theta2)

eqn = 

for K = 1 : 50
  result(K) = vpasolve(eqn, [theta2, theta4], [rand()*360; randn()]);
end

T2 = [result.theta2];
T4 = [result.theta4];
mask = T2 >= 0 & T2 <= 360;
T2 = T2(mask);
T4 = T4(mask);
sortrows([T2; T4].')

ans = 

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[Walter Roberson]

syms theta4 real
theta2 = sym(339.85);
C1 = sym(1.0714);
eqn = sym(pi)/2+3*cosd(theta4)-C1*cosd(theta2)-cosd(theta4-theta2)

eqn = 

for K = 1 : 50
  result(K) = vpasolve(eqn, [theta4], [randn()]);
end
T4 = [result];
sortrows(T4.')

ans = 

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