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

- 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. - The
`main()`

function is defined as the entry point of the program:cCopy code`int main() { // Code goes here return 0; }`

- 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;`

- 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: ");`

- The value of
`x`

is read from the user using the`scanf()`

function and stored in the variable`x`

:cCopy code`scanf("%lf", &x);`

- 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);`

- 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);`

- 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.

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