Help using fsolve (theta beta mach)

I need to solve for theta when M1 and beta are known, I believe this is the formula I need to translate, but I am not too proficient in matlab and unsure how to turn this into code.

How do I use f solve or another formula to solve for theta?

Answer 1

[Sam Chak]

Hi @Evan Gehret

If you have all the information on the right-hand side of the equation, then I think applying the inverse tangent (also known as arctangent) can give you the solution for θ. Look up atan and atan2.

help atan

 ATAN   Inverse tangent, result in radians.
    ATAN(X) is the arctangent of the elements of X.
 
    See also ATAN2, TAN, ATAND, ATAN2D.

    Documentation for atan
       doc atan

    Other uses of atan

       codistributed/atan    gpuArray/atan    symbolic/atan
       dlarray/atan          sym/atan         tabular/atan

help atan2

 ATAN2  Four quadrant inverse tangent.
    ATAN2(Y,X) is the four quadrant arctangent of the elements of X and Y
    such that -pi <= ATAN2(Y,X) <= pi. X and Y must have compatible sizes.
    In the simplest cases, they can be the same size or one can be a
    scalar. Two inputs have compatible sizes if, for every dimension, the
    dimension sizes of the inputs are either the same or one of them is 1.
 
    See also ATAN, ATAN2D.

    Documentation for atan2
       doc atan2

    Other uses of atan2

       codistributed/atan2    gpuArray/atan2    symbolic/atan2
       dlarray/atan2          sym/atan2         tabular/atan2
       fixedpoint/atan2

[Dyuman Joshi]

Hello @Evan Gehret , if this answer solved your problem, please consider accepting the answer.

Answer 2

[lazymatlab]

You do not need fsolve. Code below would be enough.

num = M1^2 * (sin(beta))^2 - 1;
den = M1^2 * (gamma + cos(2*beta)) + 2;
theta = atan(2 * cot(beta) * num / den);