C atan2() Function

The atan2() function in C is a standard library function that computes the arc tangent of the two variables y and x. It returns the angle whose tangent is the quotient of two specified numbers (i.e., y/x). It is part of the C standard library (math.h). This function is useful for calculating the angle between the positive x-axis of a plane and the point given by the coordinates (x, y).

Table of Contents

1. Introduction
2. atan2() Function Syntax
3. Understanding atan2() Function
4. Examples
   • Computing Arc Tangent with Two Parameters
   • Using atan2() with User Input
5. Real-World Use Case
6. Conclusion

Introduction

The atan2() function computes the arc tangent of the quotient of its two arguments. The arc tangent is the inverse of the tangent function and returns the angle whose tangent is the quotient y/x. The result is an angle in radians, taking into account the signs of both arguments to determine the correct quadrant of the angle.

atan2() Function Syntax

The syntax for the atan2() function is as follows:

#include <math.h>
double atan2(double y, double x);

Parameters:

• y: The ordinate (y-coordinate) value.
• x: The abscissa (x-coordinate) value.

Returns:

• The function returns the arc tangent of y/x in radians. The result is in the range ([- \pi, \pi]).

Understanding atan2() Function

The atan2() function computes the angle in the Euclidean plane, given the coordinates (x, y), considering the correct quadrant of the angle. This is more accurate than simply computing atan(y/x) because it accounts for the signs of both x and y.

Examples

Computing Arc Tangent with Two Parameters

To demonstrate how to use atan2() to compute the arc tangent with two parameters, we will write a simple program.

Example

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

int main() {
    double x = 1.0;
    double y = 1.0;

    // Compute the arc tangent of y and x
    double angle = atan2(y, x);

    // Print the result
    printf("Arc tangent of (%.2f, %.2f) is: %.2f radians\n", y, x, angle);

    return 0;
}

Output:

Arc tangent of (1.00, 1.00) is: 0.79 radians

Using atan2() with User Input

This example shows how to use atan2() to compute the arc tangent with two parameters provided by the user.

Example

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

int main() {
    double x, y;

    // Get user input for x and y
    printf("Enter the x-coordinate: ");
    scanf("%lf", &x);
    printf("Enter the y-coordinate: ");
    scanf("%lf", &y);

    // Compute the arc tangent of y and x
    double angle = atan2(y, x);

    // Print the result
    printf("Arc tangent of (%.2f, %.2f) is: %.2f radians\n", y, x, angle);

    return 0;
}

Output (example user input x "1.0" and y "1.0"):

Enter the x-coordinate: 1.0
Enter the y-coordinate: 1.0
Arc tangent of (1.00, 1.00) is: 0.79 radians

Real-World Use Case

Calculating Direction Angle from Coordinates

In real-world applications, the atan2() function can be used to calculate the direction angle from coordinates, such as finding the bearing angle from a point.

Example: Calculating Direction Angle from Coordinates

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

int main() {
    double x1, y1, x2, y2, delta_x, delta_y, angle;

    // Get user input for the coordinates of the two points
    printf("Enter the x-coordinate of the first point: ");
    scanf("%lf", &x1);
    printf("Enter the y-coordinate of the first point: ");
    scanf("%lf", &y1);
    printf("Enter the x-coordinate of the second point: ");
    scanf("%lf", &x2);
    printf("Enter the y-coordinate of the second point: ");
    scanf("%lf", &y2);

    // Calculate the differences in coordinates
    delta_x = x2 - x1;
    delta_y = y2 - y1;

    // Calculate the direction angle using atan2
    angle = atan2(delta_y, delta_x);

    // Print the result
    printf("The direction angle from point (%.2f, %.2f) to point (%.2f, %.2f) is: %.2f radians\n", x1, y1, x2, y2, angle);

    return 0;
}

Output (example user input coordinates (0,0) and (1,1)):

Enter the x-coordinate of the first point: 0
Enter the y-coordinate of the first point: 0
Enter the x-coordinate of the second point: 1
Enter the y-coordinate of the second point: 1
The direction angle from point (0.00, 0.00) to point (1.00, 1.00) is: 0.79 radians

Conclusion

The atan2() function is essential for computing the arc tangent with two parameters in C. It is useful in various trigonometric calculations, particularly in fields like geometry, physics, and engineering, where determining the angle between two points or vectors is required.