'''
can you provide a sample python code to approximate the sine function?
'''

import math

def sin(x, n=10):
    """
    Computes the approximation of sine function for a given angle x using the first n terms of the Taylor series.
    """
    sine = 0.0
    for i in range(n):
        sign = (-1) ** i
        numerator = x ** (2*i + 1)
        denominator = math.factorial(2*i + 1)
        sine += sign * numerator / denominator
    return sine

# Example usage
x = math.pi/4
print("sin({}) = {}".format(x, sin(x)))  # Output: sin(0.7853981633974483) = 0.7071067811865476

sin(x) ≈ x - x^3/3! + x^5/5! - x^7/7! + ... + (-1)^n * x^(2n+1) / (2n+1)!