Day 57: Python Program to Find Sum of Cosine Series

 import math

def cosine_series_sum(x, n):

    """

    Calculate the sum of the cosine series up to n terms for a given x.

    :param x: The angle in radians

    :param n: The number of terms in the series

    :return: The sum of the cosine series

    """

    cosine_sum = 0

    sign = 1  

    for i in range(n):

        term = sign * (x**(2 * i)) / math.factorial(2 * i)

        cosine_sum += term

        sign *= -1  

     return cosine_sum

x = float(input("Enter the value of x (in radians): "))

n = int(input("Enter the number of terms in the series: "))

result = cosine_series_sum(x, n)

print(f"The sum of the cosine series up to {n} terms for x = {x} is: {result}")

#source code --> clcoding.com 

Code Explanation:

Import Statement

import math

Imports the math module, which provides mathematical functions like math.factorial().

Function Definition: cosine_series_sum()

def cosine_series_sum(x, n):

    """

    Calculate the sum of the cosine series up to n terms for a given x.

    

    :param x: The angle in radians

    :param n: The number of terms in the series

    :return: The sum of the cosine series

    """

Purpose: Defines a function to compute the cosine of an angle using its Taylor series expansion.

Parameters:

x: The angle in radians.

n: The number of terms in the series.

Returns: The computed cosine value as the sum of the series.

Initialize Variables

    cosine_sum = 0

    sign = 1

cosine_sum: Initializes the sum to 0.

sign: Tracks the alternating signs (+1,−1,+1,−1,…) in the series.

For Loop to Compute Series

    for i in range(n):

Iterates through 𝑛

n terms of the cosine series.

Calculate Each Term

        term = sign * (x**(2 * i)) / math.factorial(2 * i)

Computes each term in the Taylor series:𝑥2 𝑖x 2i Raises x to the power 

2i (only even powers for cosine).

(2i)!: Computes the factorial of 

2i using math.factorial().

sign: Alternates between +1 and −1 for successive terms.

 

Add Term to Sum

        cosine_sum += term

Adds the computed term to the cumulative sum.

Alternate the Sign

        sign *= -1

Multiplies sign by −1to alternate between 

+1 and −1 for the next term.

Return the Result

    return cosine_sum

Returns the final sum of the cosine series.

Input the Angle and Number of Terms

x = float(input("Enter the value of x (in radians): "))

n = int(input("Enter the number of terms in the series: "))

Prompts the user to:

Enter the angle (𝑥 )in radians.

Enter the number of terms (𝑛)for the series.

Call the Function

result = cosine_series_sum(x, n)

Calls the cosine_series_sum() function with the provided inputs.

Stores the result in the variable result.

Output the Result

print(f"The sum of the cosine series up to {n} terms for x = {x} is: {result}")

Formats and displays the result using an f-string.