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

 sine-series

Expanding the above notation, the formula of Sine Series is

sine-series1

For example,

 Let the value of x be 30.

 radian

So, Radian value for 30 degree is 0.52359.

sine

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.

  1. Converting ‘x’ to radian value

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

  1. It assigns t=x and sum=x (i.e. t=0.785398 and sum=0.785398)
  2. 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.

  1. Finally it prints The value of  Sin(0.785398) = 0.7071
  1. Thus program execution is completed.

Output:

sine series

TO DOWNLOAD THE PROGRAM CODE : CLICK HERE

 

13 Responses

  1. sahil says:

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

  2. Rex says:

    can you put the C++ program for the same question?
    it would really help me if you do.

  3. Amso says:

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

  4. Irf says:

    Amazing explanation!

  5. naveen says:

    amazing explanation

  6. Falit kumar says:

    Amazing

  7. Joshna says:

    Is very good

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