Implementing sin in numpy with a taylor series

sin_taylor.py

import numpy as np
from math import factorial

def sin(x):
    val = np.float64(0)
    for n in range(0, 25):
        term = (((-1) ** n) * (x ** (2*n+1)) / factorial(2*n + 1))
        val += term
        print("for x_{0}, term is {1}, sin({2}) approximation is {3}".format(
            n, term, x, val))
    return val

pi = np.float64(3.1415926)
pi = pi + sin(pi)

if __name__ == "__main__":
    vals = np.array([0, pi / 4., pi / 2., pi * 3./4., pi], dtype=np.float64)
    for n in vals:
        print("sin({0}) = {1}".format(n, sin(n)))