Trying to plot a fitted cosine sq function to data, but it won't plot properly

Question

I've followed several examples I found online but I still don't get a smooth fitted curve and I'm not sure why. The curve should mostly follow the data points however the frequency is a lot higher and just doesn't seem to be working and I'm not sure why. Not sure what else to say, I'm just a bit lost..

import scipy as sp
import matplotlib.pyplot as plt
from scipy import linalg, optimize

X=sp.array([0.0,15.0,30.0,45.0,60.0,75.0,90.0,105.0,120.0,135.0,150.0,165.0,180.0,195.0,210.0,225.0,240.0,255.0,270.0,285.0,300.0,315.0,330.0,345.0,360.0])
Y=sp.array([196.3,282.0,337.0,347.0,312.0,240.0,152.0,69.0,15.3,1.1,33.0,105.4,195.4,195.4,286.0,345.0,362.0,256.0,162.0,75.0,14.9,1.3,35.1,105.2,194.9])

#DEBUG-------------------
print("Y len: ",len(Y))
print("X len: ",len(X))
#------------------------

def fit_func(x,a,c):
    cosinesquare =  a*sp.cos(x+c)**2
    return cosinesquare

po, po_cov = sp.optimize.curve_fit(fit_func, X, Y, p0=[50,360])

#DEBUG------------------
print("po:",po)
print("po[0]: ",po[0])
print("po[1]: ",po[1])
#-----------------------

plt.scatter(X, Y, marker="x", label="Data")
plt.plot(X,fit_func(X, *po), label="Fitted func")
plt.xlabel("Angle of transmission axis")
plt.ylabel("voltage (mV)")
plt.grid()
plt.legend()
plt.show()

,

Answer 1

The other answer works, but the real issue is that you need to convert from degrees to radians. You can add sp.pi/180 to do the conversion in your function.

import scipy as sp
import matplotlib.pyplot as plt
from scipy import linalg, optimize

X=sp.array([0.0,15.0,30.0,45.0,60.0,75.0,90.0,105.0,120.0,135.0,150.0,165.0,180.0,195.0,210.0,225.0,240.0,255.0,270.0,285.0,300.0,315.0,330.0,345.0,360.0])
Y=sp.array([196.3,282.0,337.0,347.0,312.0,240.0,152.0,69.0,15.3,1.1,33.0,105.4,195.4,195.4,286.0,345.0,362.0,256.0,162.0,75.0,14.9,1.3,35.1,105.2,194.9])

#DEBUG-------------------
print("Y len: ",len(Y))
print("X len: ",len(X))
#------------------------

def fit_func(x,a,c):
    cosinesquare =  a*sp.cos((x+c)*sp.pi/180.)**2
    return cosinesquare

po, po_cov = sp.optimize.curve_fit(fit_func, X, Y, p0=[50,360])

#DEBUG------------------
print("po:",po)
print("po[0]: ",po[0])
print("po[1]: ",po[1])
#-----------------------

plt.scatter(X, Y, marker="x", label="Data")
plt.plot(X,fit_func(X, *po), label="Fitted func")
plt.xlabel("Angle of transmission axis")
plt.ylabel("voltage (mV)")
plt.grid()
plt.legend()
plt.show()