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 codeint 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 codedouble x, result;
4. The user is prompted to enter the value of x in radians using the printf() function:cCopy codeprintf("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 codescanf("%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 coderesult = 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 codeprintf("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.

Input/Output