from math import *
from numpy import *
from matplotlib.pylab import *


def g(x, n):
	s = 0
	for j in range(n+1):
		s += ((-1)**j *x**(2*j+1.0))/factorial(2*j + 1)
	return s

x = linspace(0, 4*pi, 20)
n_list = (1, 2, 3, 6, 12)

for n in n_list:
	plot(x, g(x, n))


plot (x,sin(x))
ylabel ("f(x, n)")
xlabel ("x")
ylim(-5,5)
legend (["((-1)**j *x**(2*j+1))/factorial(2*j + 1)", "sin(x)"])
show()