C program for Cosine Series

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

Cosine Series:

                Cosine Series is a series which is used to find the value of Cos(x).

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

The formula used to express the Cos(x) as Cosine Series is

cosine_series

Expanding the above notation, the formula of Cosine Series is

cosine_series1

For example,

                Let the value of x be 30.

 radian

So, Radian value for 30 degree is 0.52359.

cosine_series2

So, the value of Cos(30) is 0.8660.

Program code for Cosine Series in C:

#include<stdio.h>
#include<conio.h>

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

Related: C program for Sine 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 Cos(x) is calculate.
  • Finally the value of Cos(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 4.

  1. Converting ‘x’ to radian value

x = x * 3.14159 / 180    (x = 30 * 3.14159 / 180)    So,  x=0.52359

  1. It assigns t=1 and sum=1
  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 = (1 * (-1) * 0.52359 * 0.52359)/(2 * 1 * (2 * 1 – 1))

So,  t = – 0.13707

sum = 1 + (- 0.1370)

So,  sum=0.86293

i++

So,  i=2

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

t = (- 0.13707 * (-1) * 0.52359 * 0.52359)/(2 * 2 * (2 * 2 – 1))

So,  t = 0.00313

sum = 0.86293 + 0.00313

So,  sum=0.86606

i++

So,  i=3

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

t = (0.00313 * (-1) * 0.52359 * 0.52359)/(2 * 3 * (2 * 3 – 1))

So,  t = – 0.000028

sum = 0.86606 + (- 0.000028)

So,  sum=0.86603

i++

So,  i=4

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

t = (-0.000028 * (-1) * 0.52359 * 0.52359)/(2 * 4 * (2 * 4 – 1))

So,  t = 0.000000137

sum = 0.86603 + 0.000000137

So,  sum=0.866030137

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  Cos(0.52359) is : 0.8660
  1. Thus program execution is completed.

Output:

cosine series

TO DOWNLOAD THE PROGRAM CODE : CLICK HERE

 

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