# C Program to Calculate the Value of cos(x)

This C program calculates the value of cos(x) using the Taylor series expansion. It takes the value of x as input and provides the corresponding cosine value as output.

The cosine function, usually denoted as `cos(x)`, is a mathematical function that maps an angle `x` to the ratio of the length of the adjacent side to the hypotenuse in a right triangle. In simpler terms, it calculates the cosine value of an angle.

## Program Statement

Program Statement: Write a C program that prompts the user to enter an angle in radians (x), calculates the value of cos(x), and displays the result on the screen.

## C Program to Calculate the Value of cos(x)

```#include <stdio.h>
#include <math.h>

double calculateCos(double x, int n) {
double result = 1.0;  // Initialize the result as 1.0
double term = 1.0;    // Initialize the first term as 1.0

for (int i = 1; i <= n; i++) {
term = term * (-1) * x * x / ((2 * i) * (2 * i - 1));
result += term;
}

return result;
}

int main() {
double x;
int n;

printf("Enter the value of x: ");
scanf("%lf", &x);

printf("Enter the number of terms to be used: ");
scanf("%d", &n);

double cosine = calculateCos(x, n);

printf("cos(%.2lf) = %.4lf\n", x, cosine);

return 0;
}
```

## How it works

1. The program begins by including the necessary header files:cCopy code`#include <stdio.h> #include <math.h> `The `stdio.h` header is required for input/output operations, and the `math.h` header provides mathematical functions, including the `cos()` function.
2. The `main()` function is defined as the entry point of the program:cCopy code`int main() { // Code goes here return 0; }`
3. Inside the `main()` function, the variables `x` and `result` are declared as `double` to hold the user input and the calculated result, respectively:cCopy code`double x, result;`
4. The user is prompted to enter the value of `x` in radians using the `printf()` function:cCopy code`printf("Enter the value of x in radians: ");`
5. The value of `x` is read from the user using the `scanf()` function and stored in the variable `x`:cCopy code`scanf("%lf", &x);`
6. The `cos()` function from the math library is used to calculate the cosine of `x`, and the result is assigned to the variable `result`:cCopy code`result = cos(x);`
7. Finally, the calculated result is displayed on the screen using the `printf()` function. The format specifier `%.2f` is used to display the value of `x` with two decimal places, and `%.4f` is used to display the value of `result` with four decimal places:cCopy code`printf("The value of cos(%.2f) is %.4f\n", x, result);`
8. The `return 0;` statement indicates the successful execution of the program, and the `main()` function ends.

When the program is run, it prompts the user to enter the value of `x` in radians. After the user enters a value, the program calculates the cosine of `x` using the `cos()` function and displays the result on the screen with the specified precision.