Tring to solve for a transcendental equation

Hi,

I am tring to solve a transcendental equation.

L=0:.005:.15;
syms eigen
Bi=(100*L)/1.5
eigen=Bi/tan(eigen)

I want to find the value for eigen. I have not been able to figure out how to do this. All I have gotten is it outputting equations. How can I go about this to solve for eigen.

Thanks

Answer 1

[Alan Stevens]

You can rearrange the equation as eigen*tan(eigen) = Bi and use fzero as below. However, because of the nature of tan, your results will depend on your initial guesses.

L=0:.005:.15;
Bi=(100*L)/1.5;

eigen = zeros(1,numel(L));
eig = 1;   % Initial guess
for i = 1:numel(L)
    
    eigen(i) = fzero(@(eig) efn(eig,Bi(i)),eig); 
    
end

function Z = efn(eig, Bi)

        Z = eig*tan(eig) - Bi;
end