how to solve equation to find angle

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Megha
Megha 2020-8-29
编辑： Ayush 2024-11-6，5:29
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.
  2 个评论
Alan Stevens
Alan Stevens 2020-8-29
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
VBBV 2020-9-8
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

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回答（1 个）

Ayush
Ayush 2024-11-6，5:28
编辑：Ayush 2024-11-6，5:29
Ran in:
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.

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