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Finding an angle in a trigonometric function using 2 equations

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Hello everybody,
I am trying to find beta angle in the eqns. below. I tried "vpasolve, linsolve, solve" but none of them seem to work.
syms M gamma
M=7.0;
gamma=1.3;
x=0:(0.01):2;
dy=((2.25+4*x-x.^2).^(-1/2)).*(2-x);
beta = solve(dy==2/cotd(beta)*((M.^2*sin(beta.^2)-1)/(M.^2*(gamma+cos(beta)^2)+2)), beta)
pressureratio= 1+(2*gamma)/(gamma+1)*((M*sind(beta)).^2-1)
I always end up getting a different error message. Is there a way to find beta?
  2 Comments
Dyuman Joshi
Dyuman Joshi on 23 Mar 2024
You have not provided M and gamma values.
Also, gamma is a inbuilt function in MATLAB. Best to not name variables (or scripts for that matter) using function names. You could use k instead.
"I tried "vpasolve, linsolve, solve" but none of them seem to work."
In order to use solve or vpasolve, you need to specify the variable (to solve for) as a symbolic variable. See - syms. And you need to solve for each equation separately.
Also, as this equation is clearly non-linear, linsolve will not work here.
ERCAN UMUT
ERCAN UMUT on 23 Mar 2024
Edited: ERCAN UMUT on 23 Mar 2024
Oh, sorry about the insufficient information. Of course I specified gamma and used sym. I thought these equations would be enough to explain the problem I have. I updated the first message.
Yes, problem is non-linear and I wanted to solve it without any numerical scheme. Is it possible?

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Answers (1)

Dyuman Joshi
Dyuman Joshi on 23 Mar 2024
As you are solving for beta, you have to define beta as a symbolic variable.
Also, I have reduced the step size in x, as the variation for smaller values of x (and thus dy) is minute.
syms beta
M=7.0;
k=1.3;
x=0:(0.1):2;
dy=((2.25+4*x-x.^2).^(-1/2)).*(2-x);
n = numel(x);
%Pre-allocate output variable
out = zeros(1,n);
%Svoling equations separately
for r = 1:n
eqn = dy(r)==2/cotd(beta)*((M.^2*sin(beta.^2)-1)/(M.^2*(k+cos(beta)^2)+2));
out(r) = vpasolve(eqn, beta);
end
out
out = 1x21
-227.2711 -226.9536 -226.9409 -226.9413 -226.9416 -226.9418 -226.9420 -226.9421 -226.9423 -226.9424 -226.9425 -226.9426 -226.9427 -226.9428 -226.9429 -226.9430 -226.9430 -226.9431 -226.9432 -226.9433 -226.9434
pressureratio = 1+(2*k)/(k+1)*((M*sind(out)).^2-1)
pressureratio = 1x21
29.7585 29.4524 29.4402 29.4406 29.4408 29.4410 29.4412 29.4414 29.4415 29.4416 29.4417 29.4418 29.4419 29.4420 29.4421 29.4422 29.4422 29.4423 29.4424 29.4425 29.4425
  3 Comments
ERCAN UMUT
ERCAN UMUT on 23 Mar 2024
You are right and I am so sorry about the sloppiness. I had spent so much time with the code I wrote them again and again, and When I had the time I wanted post it in here so I wrote them again in a hurry which was not correct form of the equation. So sorry about that.
Your assumption is kinda correct, because MATLAB was giving error in the usage of * and ^ so I had to put a dot in front of them and when I made the changes I probably did some copy paste errors. The equation can be seen in the figure below.
I would really appreciate the help. Thank you again.
ERCAN UMUT
ERCAN UMUT on 23 Mar 2024
Edited: ERCAN UMUT on 23 Mar 2024
Thank you so much for the answer. I used the code after fixing the equation. It looks like it works but I will be able to check it tomorrow.
Thank you again.

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