def float_mod(x,a):
    k = int(x/a)
    if (x*a) < 0:
        k -= 1
    return x - float(k)*a


def ratio_based_sinus(x):
    epsilon = 1.0e-16
    last = x
    retval = x

    n = 1
    while 1:
        n += 2
        last *= (-x*x) / ( n * (n - 1) )
        retval += last

        if abs(last) < epsilon:
            break

    return retval


def final_sin(x):
    two_pi = 6.2831853
    one_pi = 3.1415926
    x = float_mod( x, two_pi )  # wrap it around, reduce range to (0,2*pi)

    if x > one_pi:      # reduce range to (0,pi)
        return -ratio_based_sinus(x - one_pi)
    else:
        return ratio_based_sinus(x)



# Test
import math

theta = 1.50
v1 = final_sin(theta)
v2 = math.sin(theta)

print "our-sin:    ", v1
print "math.sqrt():", v2