# Find the Sum of Sine Series in Python

In this article, we will learn how to find the sum of the sine series using Python. To implement this problem we will use the math module.

Sine series is an infinity series. So we will calculate the sum of the sine series for the first n terms.

Sine Formula:

sinx = x – (x³/3!) + (x^5/5!) – (x^7/7!)+ …..

x is the value of the angle in radian.

Example

```Input: n = 10
x = 30
Output: 0.5001825021996699```

## Python program for Calculating the Sum of the Sine Series

1. Import the necessary modules (i.e. import math).

2. Get user input.

3. Declare sign variable to keep track of the alternative signs in the sine series.

4. Convert user input x (i.e. degree) to radian.

5. Use the factorial() method in the math module to calculate the factorial.

6. Finally, apply the sine formula.

```import math
def sine_sum(n, x):
result = 0
for i in range(n):
sign = pow(-1, i)
pi = 22/7
angle = x*(pi/180)
result += ((pow(angle, (2.0*i+1)))/math.factorial(2*i+1))*sign

return result
n = int(input("Enter the number of items(n): "))
x = int(input("Enter the angle in degree(x): "))
print("The sum of the series is ", sine_sum(n, x))```

Output

```Enter the number of items(n): 20
Enter the angle in degree(x): 60
The sum of the series is 0.8662360750607194

Enter the number of items(n): 10
Enter the angle in degree(x): 30
The sum of the series is 0.5001825021996699

Enter the number of items(n): 10
Enter the angle in degree(x): 90
The sum of the series is 0.999999800133368```

Also, refer: