# 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 Expanding the above notation, the formula of Cosine Series is For example,

Let the value of x be 30.

So, Radian value for 30 degree is 0.52359. 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: 1. Satya says: