[2010-01] approximating sine using an identity and knowledge that sin(x) ~= x for small values of x

sin_approx.py

#!/usr/bin/env python3.0
import sys
from fractions import Fraction
from math import sin, pi

def xsin(x, threshold=.05):
	"""Sine approximation."""
	
	if abs(x) < threshold:
		return(x)
	else:
		return(3 * xsin(x / 3) - 4 * (xsin(x / 3) ** 3))

def main(*args):
	print("   x      sin   xsin    ∆  ")
	print("------- ------ ------ ------")
	
	for twelfths in range(-24, 24 + 1):
		pis = Fraction(twelfths, 12)
		x = pi * pis
		xsin_x = xsin(x)
		sin_x = sin(x)
		diff = abs(xsin_x - sin_x)
		
		if pis == 0:
			pretty = "  0    "
		elif pis.denominator == 1:
			pretty = "{0.numerator:3d}   π".format(pis)
		else:
			pretty = "{0.numerator:3d}/{0.denominator:<2d}π".format(pis)
		
		print("{pretty} {sin_x:6.3f} {xsin_x:6.3f} {diff:6.3f}".format(**locals()))

if __name__ == "__main__": sys.exit(main(*sys.argv[1:]))