 # C Program to find sum of Cos(x) series

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".

## What is the cos x series?

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.

## What is the syntax of for loop?

The syntax of a for loop is given by

``````

{
// 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.

### ALGORITHM

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) .

## C Source Code

```                                          ```#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() */```
```

## OUTPUT

```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```
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