How to Compute the Cosine Series Sum Using Python

Submitted by razormist on Thursday, August 7, 2025 - 23:41.

In this tutorial, we will learn how to program "How to Compute the Cosine Series Sum Using Python." The objective is to accurately calculate the cosine series value based on the given input. This tutorial will guide you step by step through the entire process of computing the cosine series sum. By the end of this tutorial, you will have a solid understanding of how to implement this task effectively, helping you strengthen your problem-solving abilities and enhance your Python coding skills.

This topic is straightforward to understand. Just follow the instructions provided, and you will be able to complete it with ease. The program will guide you step by step through the process of calculating the cosine series sum. So, let’s dive into the coding process!

Getting Started:

First you will have to download & install the Python IDLE's, here's the link for the Integrated Development And Learning Environment for Python https://www.python.org/downloads/.

Creating Main Function

This is the main function of the application. The following code will display a simple GUI in terminal console that will display program. To do this, simply copy and paste these blocks of code into the IDLE text editor.

import math
def cosine(x,n):
    cosx = 1
    sign = -1
    for i in range(2, n, 2):
        pi=22/7
        y=x*(pi/180)
        cosx = cosx + (sign*(y**i))/math.factorial(i)
        sign = -sign
    return cosx
 
while True:
    print("\n=============== Compute the Cosine Series Sum ===============\n")
 
    x=int(input("Enter the value of x in degrees: "))
    n=int(input("Enter the number of terms: "))
    print(round(cosine(x,n),2))
 
    opt = input("\nDo you want to try again? (yes/no): ").strip().lower()
    if opt == 'no':
        print("Exiting program....")
        break
    elif opt != 'yes':
        print("Invalid input. Exiting program....")
        break

This Python program computes the cosine of a given angle using the cosine series expansion. It prompts the user to enter an angle in degrees and the number of terms to include in the series. The angle is converted to radians, and the cosine value is calculated using the formula: cos(x) = 1 − x²/2! + x⁴/4! − x⁶/6! + ..., alternating the sign for each term. The result is rounded to two decimal places and displayed to the user. The program runs continuously, giving the option to perform multiple calculations or exit based on the user's input.

Output:

There you have it we successfully created How to Compute the Cosine Series Sum Using Python. I hope that this simple tutorial help you to what you are looking for. For more updates and tutorials just kindly visit this site. Enjoy Coding!

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