# Python Program to find the sum of sine series

In this simple python program, we need to compute the sum of sine values. It is a number-based python program.

For a better understanding of this example, we always recommend you to learn the basic topics of Python programming listed below:

## What is a sine series?

In this Python program, we need to find the sum of the 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?

We have to apply this logic in our python programming, as we accept the value of x in degree 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 we 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.

## 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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