# C program for Sine Series

Before going to the program for *Sine Series* first let us understand what is a *Sine Series**?*

**Sine Series:**

*Sine Series* is a series which is used to find the value of Sin(x).

where, **x** is the angle in **degree** which is converted to **Radian**.

The formula used to express the Sin(x) as Sine Series is

Expanding the above notation, the formula of Sine Series is

For example,

Let the value of **x **be** 30**.

So, Radian value for **30** degree is **0.52359.**

So, the value of **Sin(30)** is **0.5.**

## Program code for Sine Series in C:

#include<stdio.h> #include<conio.h> void main() { int i, n; float x, sum, t; clrscr(); printf(" Enter the value for x : "); scanf("%f",&x); printf(" Enter the value for n : "); scanf("%d",&n); x=x*3.14159/180; t=x; sum=x; /* Loop to calculate the value of Sine */ for(i=1;i<=n;i++) { t=(t*(-1)*x*x)/(2*i*(2*i+1)); sum=sum+t; } printf(" The value of Sin(%f) = %.4f",x,sum); getch(); }

**Related: C program for Cosine Series**

## Working:

- First the computer reads the value of ‘x’ and ‘n’ from the user.
- Then ‘x’ is converted to radian value.
- Then using for loop the value of Sin(x) is calculate.
- Finally the value of Sin(x) is printed.

**Related: C program for Exponential Series**

## Step by Step working of the above Program Code:

Let us assume that the user enters the value of ‘x’ as **45** and ‘n’ as **4.**

- Converting ‘x’ to radian value

x = x * 3.14159 / 180 (x = 45 * 3.14159 / 180) So, **x=0.785398**

- It assigns t=x and sum=x (i.e.
**t=0.785398**and**sum=0.785398**) - It assigns the value of
**i=1**and the loop continues till the condition of the for loop is true.

3.1. i<=n (**1<=4**) for loop condition is true

t = (0.785398 * (-1) * 0.785398 * 0.785398)/(2 * 1 * (2 * 1 + 1))

So, **t = – 0.08074**

sum = 0.785398 + (- 0.08074)

So, **sum=0.70465**

i++

So, **i=2**

3.2. i<=n (**2<=4**) for loop condition is true

t = (- 0.08074 * (-1) * 0.785398 * 0.785398)/(2 * 2 * (2 * 2 + 1))

So, **t = 0.00249**

sum = 0.70465 + 0.00249

So, **sum=0.70714**

i++

So, **i=3**

3.3. i<=n (**3<=4**) for loop condition is true

t = (0.00249 * (-1) * 0.785398 * 0.785398)/(2 * 3 * (2 * 3 + 1))

So, **t = – 0.000032**

sum = 0.70714 + (- 0.000032)

So, **sum=0.707108**

i++

So, **i=4**

3.4. i<=n (**4<=4**) for loop condition is true

t = (- 0.000032 * (-1) * 0.785398 * 0.785398)/(2 * 4 * (2 * 4 + 1))

So, **t = 0.000000274**

sum = 0.707108 + 0.000000274

So, **sum=0.707108274**

i++

So, **i=5**

3.5. i<=n (**5<=4**) for loop condition is false

It comes out of the for loop.

- Finally it prints
**The value of Sin(0.785398) = 0.7071**

- Thus program execution is completed.

## Output:

### TO DOWNLOAD THE PROGRAM CODE : CLICK HERE

why didn’t we use -1.0 instead of pow((double)(-1),(double)(2*i-1))

Hi Sahil, We can use -1.0 instead of pow((double)(-1),(double)(2*i-1)). I have tired it and it works.

Also thanks for asking such a good question..

can you put the C++ program for the same question?

it would really help me if you do.

Hi Rex,

Based on your request, I have put the post:

C++ program for sine series.hope it would help you.. 🙂

Very good

Thank you kuldeep.. 🙂

Very consistent, clear and basic explaination so that everyone can understand without much effort.

Amazing explanation!