Cosine or Cosx is defined as a trigonometric angle function in a right angle triangle, For a better understanding of this cosine C program example, we always recommend you to learn the basic topics of C programming listed below:

In this C program, we have to find the value of **Cosine X** up to the given accuracy. The **Trigonometric** functions would use to relate the angles of a triangle to its sides. **Cosine** which we call as **Cos x** is the ratio of adjacent side length to Hypotenuse length. "**cos A = adjacent side / hypotenuse**", normally **Cos x** values come opposite as **Sine x** which means **Cos 0 = 1, Cos 90 = 0**.

Here in this c program, we convert the value which we accept from the user in **degrees** to **radians**. We also get the accuracy from the user's input. In this c program, we are using a `do-while`

** **loop for calculating the value of the **cos x** using the equations. In that `do-while`

** **loop. after accepting the value of the angle in degree, we convert that value to radians. Then we accept the accuracy needed for the **cos x**. We assign the term as one and **cos x** as the term and then** n** as **1**.

Open a** '**`do-while`

**'**loop till the condition is a match (**acc <= fabs(cosval - cosx)**) then we calculate the value of **den** as **2*n*(2*n-1)**, which uses the formula for finding the term as **-term * x * x / den**. Then we find the **cos x** using the formula **cosx + term**. Moreover, increment the **n** by **one**. Finally, we display the result using the `printf`

statement.

**STEP 1:** Import the Header libraries to use the built-in functions used in the C program.

**STEP 2:** Declare and Define the variables used in the C program, including the value of **Cos x**.

**STEP 3:** Accept the value of the angle in Degree using the `printf `

and `scanf`

statements.

**STEP 4:** Convert the value of **Degree** to **Radians** using the formula.

**STEP 5:** Accept the accuracy from the user using `printf`

and `scanf`

.

**STEP 6:** Now assign the value for **term = 1**, **cosx = term** and **n = 1**.

**STEP 7:** Open a '`do while`

'** **loop till the condition meets using C syntax.

**STEP 8:** Inside the loop, calculate the value of '**den**'

**STEP 9:** The value of **Cos x** is calculated using '**term**' and increment the **n** by **1**.

**STEP 10:** Print the result of **Cos x** using the `printf`

built-in function in C programming.

` ````
#include <stdio.h>
#include <math.h> /* include header files for accessing libraries */
#include <stdlib.h>
void main() {
int n, x1;
float acc, term, den, x, cosx = 0, cosval; /* declares cosx cosval etc variables */
printf("Enter the value of x (in degrees)\n"); /* accepts value of x in degree */
scanf("%f", & x);
x1 = x;
x = x * (3.142 / 180.0); /* Converting user input value from degrees to radians*/
cosval = cos(x);
printf("Enter the accuracy for the result\n");
scanf("%f", & acc);
term = 1;
cosx = term;
n = 1;
do {
den = 2 * n * (2 * n - 1);
term = -term * x * x / den; /* doing calculations inside the do while loop as same as sinx, please refer the sinx program for details */
cosx = cosx + term;
n = n + 1;
}
while (acc <= fabs(cosval - cosx));
printf("Sum of the cosine series = %f\n", cosx);
printf("Using Library function cos(%d) = %f\n", x1, cos(x));
} /*End of main() */
```

Enter the value of x (in degrees) 30 Enter the accuracy for the result 0.000001 Sum of the cosine series = 0.865991 Using Library function cos(30) = 0.865991 RUN 2 Enter the value of x (in degrees) 45 Enter the accuracy for the result 0.0001 Sum of the cosine series = 0.707031 Using Library function cos(45) = 0.707035