Help using fsolve (theta beta mach)

I have a disgusting equation that needs to be solved for another variable:

tand(theta) = 2*atand(beta)*(M^2*sind(beta)^2-1)/(M^2*(1.4+cosd(2*beta))+2)

I need it to be solved for beta with theta and M known.

How do I use fsolve to solve for that equation?

Answer 1

[Star Strider]

The fsolve function is a root-finding algorithm, so the search must be for zeros of the function. The function needs to be expressed in that context —

f = @(beta,theta,M) tand(theta) - 2*atand(beta).*(M.^2*sind(beta).^2-1)./(M.^2.*(1.4+cosd(2*beta))+2);
theta = 30;
M = 42;
beta0 = 180*rand;                                                                               % Can Be Anything
betav = fsolve(@(beta)f(beta,theta,M), beta0)

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

betav = 174.7907

NOTE — Since this is a trigonoometric equation, there could be an infinity of solutions, integer multiples of 360°.

.

Answer 2

[David Hill]

syms theta;
beta=35;M=1.3;%example
eqn=tand(theta) == 2*atand(beta)*(M^2*sind(beta)^2-1)/(M^2*(1.4+cosd(2*beta))+2);
vpasolve(eqn)