In this C program, we have to find the Sum of **cos(x)** Series. The Trigonometric capacity is utilized to relate the edges of a Triangle to its Sides. Cosine, which we call **cosx**, is the proportion of Adjacent side length to Hypotenuse length. "**cosA = Adjacent/ Hypotenuse**".

The cos X Series contains even powers and Factorials. Generally the formula of Cosine Series is "**cosx = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + .........."**. In this C program, we accept the input from the user in Degrees and Convert it to Radians to make calculations. Then we open a For loop and we use the formula "** cosx = cosx + (pow (x,i) /fact) *sign ; sign = sign *(-1); **to calculate the sum of the **cos x**. For using the function **pow()**, we have to include the '**math.h**' header file in this program. It is a simple program to understand. Here we use for loop.

The syntax of a for loop is given by

```
for (initializationStatement; testExpression; updateStatement)
{
// codes
}
```

Here the initialization statement is executed only once. Initially, the test expression is evaluated. If the test expression is False, then `for loop`

is terminated. But if the test expression is True, then code inside the `for loop`

is executed and update the expression. This process continues until the test expression is False. This type of loop is commonly used when the number of iterations is already known.

**STEP 1:** Include the Header files to use the built-in functions in the C program.

**STEP 2:** Declare the integer variables **n, x1, i, j**.

**STEP 3:** Declare the variables **x**, **sign**, **cosx**, **fact** as type Float.

**STEP 4:** Read the number of terms in the Series to **n**.

**STEP 5: **Read the value of '**x**' into the variable '**x**'.

**STEP 6:** Assign **x1=x**.

**STEP 7:** **x=x*(3.142/180.0)**

**STEP 8:** Assign **cosx=1** and **sign=-1** and** i=2**.

**STEP 9:** By using `for loop`

with the condition '**i<=n**' do step 10.

**STEP 10:** **fact=1**.

**STEP 11:** Assign **j=1**.

**STEP 12:** By using for loop with condition **j<=i** do step 13.

**STEP 13:** **fact=fact*j**.

**STEP 14:** Increment **j** by **1**, and do step 12.

**STEP 15:** **cosx=cosx+(pow(x,i)/fact)*sign**.

**STEP 16:** **sign=sign*(-1)**.

**STEP 17:** Increment '**i'** by **1** and do step 9.

**STEP 18:** Display the sum of the cosine series is **cosx**.

**STEP 19:** Display the value of **cos(x1)** using library function** cos(x)** .

` ````
#include<stdio.h>
#include<math.h>
void main() {
int n, x1, i, j;
float x, sign, cosx, fact;
printf("Enter the number of the terms in a series\n"); /* enter the series */
scanf("%d", & n);
printf("Enter the value of x(in degrees)\n");
scanf("%f", & x);
x1 = x;
x = x * (3.142 / 180.0); /* Degrees to radians*/ /* converting the degrees into radians */
cosx = 1;
sign = -1;
for (i = 2; i <= n; i = i + 2) {
fact = 1;
for (j = 1; j <= i; j++) {
fact = fact * j;
}
cosx = cosx + (pow(x, i) / fact) * sign; /* calculating the cosx x sum */
sign = sign * (-1);
}
printf("Sum of the cosine series= %7.2f\n", cosx);
printf("The value of cos(%d) using library method = %f\n", x1,
cos(x));
} /*End of main() */
```

Enter the number of the terms in a series 5 Enter the value of x(in degrees) 60 Sum of the cosine series = 0.50 The value of cos(60) using library method = 0.499882