sin(theta) is not a variable name.
beta = 1.135e-4;
sintheta = [-0.81704 -0.67649 -0.83137 -0.73468 -0.66744 -0.43602 0.45368 0.75802 0.96705 0.99717 ];
x = [72.01 59.99 51.13 45.53 36.15 31.66 30.16 29.01 25.62 23.47 ];
Before you do ANYTHING, PLOT your data. Ask, if it is consistent with your model. The answer here, is not really.
axis([20 80 -1 1])
I drew a line at y = -0.8, which is where I would suggest the baseline for your curve should roughly lie at.
That is, what is the asymptotic value of your function as x approaches infinity? You have written it as:
sin(theta) = -1+2*sqrt(alpha/x)*exp(-beta*(x-alpha)^2)
As x gets large, this approaches -1. Yet, clearly, your data does not get anywhere near -1, and it never will. Your data approaches a value closer to -0.8, MAYBE -0.85. So your data is inconsistent with your model. That you want to call the depedent variable sin(theta) does not matter. It simply will never get anywhere near -1.
Lets look at how you might fit this with the curve fitting toolbox. remember, that you will NEED good starting values for alpha and beta.
mdl = fittype('-1+2*sqrt(alpha./x).*exp(-beta*(x-alpha).^2)','indep','x');
fittedmdl = fit(x',sintheta',mdl,'startpoint',[20,0.01])
fittedmdl(x) = -1+2*sqrt(alpha./x).*exp(-beta*(x-alpha).^2)
Coefficients (with 95
alpha = 25.82 (23.66, 27.99)
beta = 0.01954 (0.0005392, 0.03854)
Note that I estimated beta there, too, as the value for beta that you gave is also inconsistent with the data. If I try to force the model to use beta =1.135e-4;, I get garbage for a fit, far worse than what I got for the model I chose.
Now, look carefully at the curve that came out. It does not look at all like your data. The baseline is wrong. The shape of the curve in the peak is wrong.
Why do I say those shapes are "wrong"? The peak of the curve is fairly wide. It rolls over nice and slowly. And it never even manages to start coming back down, if I look at your data. But the transition region where it drops down from 1 towards -1, is VERY sharp. That means you need a relatively large value for beta, NOT one as small as you seem to think it should be. Otherwise, you cannot get a sharp transition. But with a sharp transition there, that also means the peak wants to drop down for small x, below the value of alpha. So your data is simply not consistent with that model.
I honestly don't know where you got that model. But it simply will never look like that data. Sorry. But trying to fit a square peg into a round hole tends only to damage either the peg or the hole.
(In fact, if I try to estimate the baseline from your data, it comes out to approximately -0.79, so my visual guess was pretty good.)