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<iostream.h>
#include<iomanip.h>
#include<conio.h>

void main()
{
    int i, n;
    float x, sum, t;
    clrscr();
    
    cout<<" Enter the value for x : ";
    cin>>x;
    
    cout<<" Enter the value for n : ";
    cin>>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;
    }
    
    cout<<" The value of Sin("<<x<<") = "<<setprecision(4)<<sum;
    getch();
}

Note: setprecision(4) is used to set the floating point number upto 4 decimal points.

     iomanip.h is a header file which contains the setprecision() function.

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 30 and ‘n’ as 3.

  1. Converting ‘x’ to radian value

x = x * 3.14159 / 180    (x = 30 * 3.14159 / 180)    So,  x=0.523598

  1. It assigns t=x and sum=x (i.e. t=0.523598 and sum=0.523598)
  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<=3)    for loop condition is true

t = (0.523598 * (-1) * 0.523598 * 0.523598)/(2 * 1 * (2 * 1 + 1))

So,  t = – 0.02392

sum = 0.52359 + (- 0.02392)

So,  sum=0.499678

i++

So,  i=2

3.2.   i<=n    (2<=3)    for loop condition is true

t = (- 0.0239 * (-1) * 0.523598 * 0.523598)/(2 * 2 * (2 * 2 + 1))

So,  t = 0.000327

sum = 0.499678 + 0.000327

So,  sum=0.500005

i++

So,  i=3

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

t = (0.000327 * (-1) * 0.523598 * 0.523598)/(2 * 3 * (2 * 3 + 1))

So,  t = – 0.000002

sum = 0.500005 + (- 0.000002)

So,  sum=0.500003

i++

So,  i=4

3.4.  i<=n    (4<=3)    for loop condition is false

It comes out of the for loop.

  1. Finally it prints The value of  Sin(0.523598) = 0.5
  1. Thus program execution is completed.

Output:

sine series

TO DOWNLOAD THE PROGRAM CODE : CLICK HERE

 

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