import numpy as np
import matplotlib.pyplot as plt

def sin_approx_factory(n):
	def factorial(k):
		result = 1
		for i in range(1, k + 1):
			result *= i
		return result


	def sin(x):
		result = 0
		for i in range(0, n + 1):
			#print("+ (-1)**{} * x**{} / {} ".format(i, 2*i + 1, factorial(2*i + 1)), end = "")
			result += (-1)**(i) * x**(2*i + 1) / factorial(2*i + 1)
		#print()
		return result 
	return sin


X = np.arange(-4, 4, 0.01)
plots = list()

p0, = plt.plot(X, np.sin(X), label="sin(x)")
plots.append(p0)

for i in range(5):
	p, = plt.plot(X, sin_approx_factory(i)(X), label="approx({})".format(i))
	plots.append(p)

plt.legend(handles=plots)
plt.show()