import math


# iterative factorial function
def fac(x):
    factor = 1.0
    for i in range(1, x + 1):
        factor *= i
    return factor


# approximation of the sine function using taylor series
def taylor_sine(n, x):
    k = 0.0
    sign = -1.0
    for i in range(0, n):
        sign *= -1.0
        k += sign / fac(2 * i + 1) * math.pow(x, 2 * i + 1)

    return k


def test():
    print("taylor: %s, sine: %s" % (taylor_sine(16, math.pi), math.sin(math.pi)))