Write a program to evaluate sine using taylors expansion?

Answer 1

To evaluate the sine function using Taylor's expansion, you can implement the following Python program:

import math

def sine_taylor(x, n_terms=10):
    sine_value = 0
    for n in range(n_terms):
        term = ((-1) ** n * (x ** (2 * n + 1))) / math.factorial(2 * n + 1)
        sine_value += term
    return sine_value

# Example usage
angle = math.radians(30)  # Convert degrees to radians
print(sine_taylor(angle))

This program calculates the sine of an angle x in radians by summing the first n_terms of its Taylor series expansion around zero. Adjust n_terms for higher accuracy.