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how to solve equation to find angle

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Megha
Megha on 29 Aug 2020
Commented: VBBV on 8 Sep 2020
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 Comments
Alan Stevens
Alan Stevens on 29 Aug 2020
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 on 8 Sep 2020
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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