Solving for angle (Beta) using vpasolve

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Hello I'm trying to see why I'm not getting the correct angle when i Solve for the following equation. I'm not sure if this is due to a coding error that I dont see or if has to do with an angle property like the refence angle.
The equation I'm solving for is the following the resul i get is
beta =
-196.3722
However if im not mistaken the answer i should get is 23.13 deg.
M1 = 3;
P1 = 1;
theta2 = 5;
thetha3 = 20;
gamma = 1.4;
syms beta
tantheta = tand(theta2);
x = 2*cotd(beta)*((M1^2*((sind(beta))^2)-1));
y = M1^2*(gamma+cosd(2*beta))+2;
eqn = x/y;
result = vpasolve(eqn == tantheta,beta);
beta = result

Accepted Answer

Star Strider
Star Strider on 24 Oct 2021
That’s the result I get when I solve it (and then correct it by ) —
M1 = 3;
P1 = 1;
theta2 = 5;
thetha3 = 20;
gamma = 1.4;
syms beta
tantheta = tand(theta2);
x = 2*cotd(beta)*((M1^2*((sind(beta))^2)-1));
y = M1^2*(gamma+cosd(2*beta))+2;
eqn = x/y;
result = solve(tantheta == eqn, beta);
beta = vpa(result) + 180
beta = 
23.133257450785606135761291258498
.
  5 Comments
Walter Roberson
Walter Roberson on 24 Oct 2021
vpasolve() uses a modified Newton-Raphson algorithm. It might need to take the derivative of the function internally first.
Star Strider
Star Strider on 24 Oct 2021
As always, my pleasure!
I looked at the linked Question, and posted an Answer (of sorts) to it, although I could not find a symbolic solution for it.
.

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