'''Programma per calcolare la derivata di sin(x) tra 0 e 2Pi 
tramite differenziazione numerica'''


import numpy as np


def main():

    n=input("Numero di intervalli:\n")
    n=int(n)

    h=2*np.pi/n#larghezza intervalli

    f = open("derivata_seno.dat",mode='w')
    fe = open("errore_derivata_seno.dat",mode='w')

    for i in range(n):
        x=i*h
        xp=x+h
        xm=x-h
        
        fx=np.sin(x)
        fxp=np.sin(xp)
        fxm=np.sin(xm)


        derx_exact=np.cos(x)
        derx_oh=(fxp-fx)/(h)

    
        f.write(str(x)+" "+str(derx_exact)+"  "+ str(derx_oh)+"\n")
        fe.write(str(x)+" "+str(derx_oh-derx_exact)+"\n")

    f.close()
    fe.close()

if __name__ == "__main__":
    main()