fit a custom equation of the type (sin(Alpha))^n

I have X = [5.29 15.8 26.47 37.05 47.64 58.23 68.82 79.41 90 100.58 111.17 121.76 132.35 142.94 153.52 164.11 174.7];

and Y = [0.25 0.20 0.17 0.187 0.229 0.385 0.63 0.97 1 0.89 0.67 0.42 0.24 0.18 0.16 0.24 0.30]

I would like to fit only and only sin "" equation to this data. Here, I make it claer that I do not want polyfit. Moreover, I also

want to find the value of "n" for which the equation fits the best.

This may go like,

plot(X,Y);
hold on;
for n = -2:0.1:2
Curve = fit(X,Y,'(sin(X)).^n')
end

However, this does not work. Any help!