# Python Program to find the sum of sine series

February 13, 2022, Learn eTutorial
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## What is a sine series?

In Fourier analysis, sine is a Trigonometric function of an angle. Sine series is a number series that is for finding the value of sine(x). Where ’x’ is the angle in between. The formula to find the sine(x) is denoted by

sine(x) = x * pi / 180

We further expand this sine formula and get the result as

sine(x) = x −x^3/3!+x^5/5!−x^7/7!+x^9/9!· · ·

Consider an example to understand the idea,

take the x as 30, so we have to find the value of sine(30) that is 30 * pi / 180. Where the value of pi is 3.1415

so the equation will be

Sine(30) = 30 * 3.1415 / 180 = 0.5, so the radian value of sine 30 will be 0.5, and we have to apply this value to the equation we mentioned above to get the sine series

Sine(30) = (0.5^3 / 3!) + (0.5^5 / 5!) + ….

## How to find the sum of the sine series in python?

In this Python program, we need to find the sum of the sine series. We have to apply the above logic as we accept the value of x in degrees and the number of terms, we needed in the sine series. Then we are calling a user-defined function to calculate the value of the sine series in python language. We import a module called `math` to the program, and we initialize the sine variable to zero, and open a `for loop` till the number of terms to calculate the sum of the series. Inside the loop, we have to convert the angle from degree to radian using the formula

y=x*(pi/180)

and after getting the value in radian, we have to apply the formula for the sine series in python, which is

sine = sine + ((y**(2.0*i+1))/math.factorial(2*i+1))*sign

then we return the sine value to the calling function and print the value of the sine series using the `round` method in python programming.

### ALGORITHM

STEP 1: Accept the number of terms of series and the angle in degree from the user, using the input method in python language and convert it to the integer using `int` datatype.

STEP 2: Call the user-defined function to calculate the sine series and print the return value using the `round` method in python programming basics.

USER DEFINED FUNCTION

STEP 1:  Import a `math` module to the program to use the inbuilt mathematical functions.

STEP 2:  Initialize a variable sine as 0

STEP 3: Open a `for loop` from 1 to the number using the `range` method

STEP 4: Calculate the sign using the formula (-1)**i

STEP 5: Convert the angle from degree to radian using the formula y=x*(pi/180)

STEP 6: Calculate the sine series using the formula sine + ((y**(2.0*i+1))/math.factorial(2*i+1))*sign and return the sine value to the calling function using python programming methods.

To find the sum of sine series, we are using the below concepts of python programming, please refers to these topics for a better understanding.

## Python Source Code

```                                          ```import math
def sin(x,n):
sine = 0
for i in range(n):
sign = (-1)**i
pi=22/7
y=x*(pi/180)
sine = sine + ((y**(2.0*i+1))/math.factorial(2*i+1))*sign
return sine
x=int(input("Enter the value of x in degrees:"))
n=int(input("Enter the number of terms:"))
print(round(sin(x,n),2))```
```

## OUTPUT

```Enter the value of x in degrees:30
Enter the number of terms:10
0.5```

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