Can someone help me how to calculate theta?

a and b are variables calculated by measured values.

I dont know how should I define theta:

Error

Unrecognized function or variable 'theta'.

S = solve ((((a+b)*theta)/(theta^2 - (a*b))*tan_theta), theta)

[Matt J]

Is tan_theta also known, or did you mean to write tan(theta) ?

[Image Analyst]

Somethimes it helps to plot things numerically.

% Demo by Image Analyst.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clearvars;
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 16;
fprintf('Beginning to run %s.m ...\n', mfilename);
theta =  linspace(-1.2, 1.2, 400);
a = linspace(-pi, pi, 400);
mina = min(a)
maxx = max(a)
allb = linspace(-pi, pi, 9)
for k = 1 : length(allb)
    b = allb(k);
    subplot(3, 3, k);
    plot(theta, tan(theta), 'b-', 'LineWidth', 2);
    grid on;
    hold on;
    y = (a + b) .* theta ./ (theta.^2 - a * b);
    plot(theta, y, 'r-', 'LineWidth', 2)
    caption = sprintf('b = %.2f, a = [%.2f, %.2f]', b, mina, maxx);
    title(caption);
    xlabel('theta')
end

[Walter Roberson]

    y = (a + b) .* theta ./ (theta.^2 - a * b);

if theta is 0 and a and b are finite then the numerator is 0. If neither a nor b are 0 then the denominator would be nonzero for this case. Therefore y would have to be 0. tan(0) is 0. So except when a or b are 0, theta = 0 is a solution. However none of your plots show it as a solution.

[Elham Rahimi]

a and b are values between (0.001-1.00)

tan (theta) is unknown as well

the error is "unrecognized function or variable theta"

I believe the equation is solvable since theta is the only unknown!

(tan(theta) = (a + b) .* theta ./ (theta.^2 - a * b)

[Walter Roberson]

What happens if, hypothetically, theta were 0?

tan(theta) = (a+b) * theta /(theta^2 - a*b)

tan(0) is 0

0 = (a+b) * 0 / (0^2 - a*b)
0 = 0 * (a+b) /(-a*b)

if a*b is not 0 then the denominator is not 0. 0 / nonzero is 0. So left side is 0 and right side is 0.

Therefore theta = 0 is a solution whenever neither a nor b is 0.

Answer 1

[Uba K Ubamanyu]

try fsolve with an initial guess.

I am assuming you meant to write tan(theta) instead of tan_theta

intial_guess =1;

S = fsolve(@(theta) (((a+b)*theta)/(theta^2 - (a*b))*tan(theta)), initial_guess)

[Elham Rahimi]

I got this error!

No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,

but the vector of function values is not near zero as measured by the

value of the function tolerance.

<stopping criteria details>

Unrecognized function or variable 'theta'.

-- logically the equation should be solved for theta , I think basically something is wrong with my MATLAB code, which I cannt figure it out. fsolve is not working!

Answer 2

[Walter Roberson]

The solution is theta = 0 unless a or b are 0.

[Walter Roberson]

a = randn()

a = 1.0368

b = randn()

b = -0.3255

syms theta
eqn = tan(theta) == (a+b)*theta/(theta^2 - a*b)

eqn = 

E2 = lhs(eqn) - rhs(eqn)

E2 = 

fplot([E2,0], [-20 20])

fplot([E2, 0], [-1 1])

theta = 0 is not the only solution, but it is a solution.

[Walter Roberson]

This all depends upon the equation shown in https://www.mathworks.com/matlabcentral/answers/1574133-can-someone-help-me-how-to-calculate-theta#comment_1805933 being the correct equation. The question you posted originally was different:

a = rand()

a = 0.9761

b = rand()

b = 0.8016

syms theta
E2 = (((a+b)*theta)/(theta^2 - (a*b))*tan(theta))

E2 = 

fplot([E2, 0], [-10 10])

fplot([E2, 0], [-1 1])

we can see by inspection that this has a 0 when theta is 0, or when tan(theta) is 0, or when theta is infinite.

[Elham Rahimi]

I don't know how did you draw these graphs, but when I define theta as a sym/s or symbolic it will not calculate theta. I need to calculate theta from the equation.

using this code will give me the symbolic "theta" in the rest of following equation in my code!!

eqn =

tan(theta) == (894987427786373*theta)/(4503599627370496*(theta^2 - 710587193844941/72057594037927936))

[Walter Roberson]

I showed how to plot:

E2 = lhs(eqn) - rhs(eqn)
fplot([E2,0], [-20 20])

E2 is the difference between the left hand side and the right hand side. The places where E2 is 0 are the places where the two sides balance out

[Elham Rahimi]

can you show the value for theta?

[Walter Roberson]

eqn = str2sym('tan(theta) == (894987427786373*theta)/(4503599627370496*(theta^2 - 710587193844941/72057594037927936))')

eqn = 

E2 = lhs(eqn) - rhs(eqn)

E2 = 

fplot([E2, 0], [-1 1])