how to solve equation to find angle

I have the values of variables be like:

clear;
Vau = 43.0;
Vsu = 47.45;
beta = 1.41;
gamma = 5/3;

syms theta_u

I wish to find the value of theta_u.

For this, I have an equation like

when i solved this equation it turns out to be like

Now I put this equation for solving it to matlab using code:

Q3 = double(solve(Vsu*(cosd(theta_u*(sqrt(2/(beta*gamma)))))*(1/(Vau*(cosd(theta_u))))-1))

it gives an error

Q3 = double(solve(Vsu*(cosd(theta_u*(sqrt(2/(beta*gamma)))))*(1/(Vau*(cosd(theta_u))))-1))
Warning: Unable to solve symbolically. Returning a numeric approximation instead. 
> In solve (line 304) 

Q3 =

 -162.2052

which is also a wrong answer. The correct answer is 71.8. Please suggest if there are any corrections.

[Alan Stevens]

Using fzero, I also get either 162.2052 or -162.2052 (depending on the initial guess). Why do you think the answer should be 71.8? Have you doube checked your equation and constants?

[VBBV]

Place the term in sqrt outside the cost parenthesis

Try this

Q3 = solve(sqrt((beta*gamma)/2)*acos((sin(theta_u)*Vau)/Vsu),theta_u)

You will get two values ...

Q3 =

      asin(949/860)
 pi - asin(949/860)

Multply the first real(asin(949/860)*180/pi)

To get 90 deg

Answer 1

[Ayush]

Hi @Megha

I used solve function and here is the output:

% Clear the workspace
clear;

% Given values
Vau = 43.0;
Vsu = 47.45;
beta = 1.41;
gamma = 5/3;

% Define the symbolic variable
syms theta_u

% Define the equation
equation = cos(theta_u) == (Vau * cos(theta_u) / Vsu) * sqrt(beta * gamma / 2);

% Solve the equation for theta_u
solution = solve(equation, theta_u);

% Convert the solution from radians to degrees
solution_degrees = rad2deg(vpa(solution));

% Display the solution
disp('The solution for theta_u in degrees is:');

The solution for theta_u in degrees is:

disp(vpa(solution_degrees, 4)); % Display the solution with 4 decimal places

I am also getting 90 degrees.