atan2() function in C

Introduction to atan2() Function in C

The atan2() function in C is used to compute the arc tangent of the two variables y and x.

Unlike the basic atan() function, which only takes a single argument, atan2(y, x) takes two arguments and returns the angle in radians between the positive x-axis and the point (x, y).

This function is particularly useful for converting Cartesian coordinates to polar coordinates.

Syntax atan2() Function in C:

#include<math.h> 

double atan2(double y, double x);

Example:

Program 1: Basic Usage of atan2()

// program to demonstrates the basic use of the atan2() function by calculating the angle for given y and x coordinates. 
#include <stdio.h>
#include <math.h> 

int main() {
    double y = 5.0;
    double x = 3.0;
    double angle = atan2(y, x);

    printf("The angle between the positive x-axis and the point (%.2f, %.2f) is %.2f radians\n", x, y, angle);
    return 0;
}	

Output:

The angle between the positive x-axis and the point (3.00, 5.00) is 1.03 radians

Program 2: Converting Cartesian Coordinates to Polar Coordinates

//  program to converts Cartesian coordinates (x, y) to polar coordinates (r, θ) using atan2() to compute the angle θ.
#include <stdio.h>
#include <math.h> 

int main() {
    double x = 3.0;
    double y = 4.0;
    double r = sqrt(x*x + y*y); // Calculating the radius
    double theta = atan2(y, x); // Calculating the angle

    printf("Cartesian coordinates (%.2f, %.2f) -> Polar coordinates (r: %.2f, θ: %.2f radians)\n", x, y, r, theta);
    return 0;
}			

Output:

Cartesian coordinates (3.00, 4.00) -> Polar coordinates (r: 5.00, θ: 0.93 radians)

Uses of atan2()

Converting Cartesian to Polar Coordinates: atan2() is widely used to convert (x, y) Cartesian coordinates to polar coordinates, providing a more intuitive angle measurement.

Robotics and Navigation: In robotics and navigation systems, atan2() helps determine direction and orientation by calculating angles between different points.

Computer Graphics: In graphics programming, atan2() can be used to rotate objects, calculate angles for transformations, and determine orientations of graphical entities.

Signal Processing: For phase angle calculations in complex signal processing, atan2() is essential for accurate results.

Physics Simulations: Simulations involving projectile motion, circular motion, or any scenario requiring angle calculation between vectors rely on atan2() for precision.

By understanding and using the atan2() function, programmers can accurately handle a variety of tasks involving angle calculations and coordinate transformations.