curve fitting sine to the power of python

Question

I want to fit a signal into a cos or sine function:

reference signal:

sample_rate =1000
start_time = 0
end_time = 12

t = np.arange(start_time, end_time, 1/sample_rate)
amplitude = 12 #peak to peak
period = 60/15
n= 4

func =-amplitude* np.cos( np.pi *  t/period)**(2*n) +  amplitude

And this signal must fit into model:

def fit(t, a, b, n):
    return -a * np.cos(np.pi* t/(b))**(2*int(n)) + a 

By doing:

params, pcov = scipy.optimize.curve_fit(fit, t, func, )
a, b, n = params

I am getting:

params a = 11.9; b = 0.97 and n=1

This doesn't match at all...