What is the difference between atan and atan2 in C++?

In C++, both atan and atan2 are functions used to compute the arctangent, but they have important differences in usage and functionality.

1. Parameter Count and Type:

   • The atan function accepts one parameter, which is the ratio y/x (where x is implicitly 1). Its function prototype is double atan(double x);.
   • The atan2 function accepts two parameters, y and x (where y and x represent the y-coordinate and x-coordinate of a point in the Cartesian coordinate system). Its function prototype is double atan2(double y, double x);.

2. Range of Returned Values:

   • The atan function returns an angle in the range from -π/2 to π/2 (-90 degrees to 90 degrees).
   • The atan2 function returns an angle in the range from -π to π (-180 degrees to 180 degrees). This allows atan2 to determine the exact quadrant of the point in the plane.

3. Handling x = 0:

   • When using atan, if you need to compute the angle via y/x and x is zero, you must manually handle the division by zero case.
   • atan2 automatically handles the case where x is zero, returning the correct angle (π/2 or -π/2) depending on the sign of y.

Example:

Assume we want to compute the angle of the point (0, 1) relative to the positive x-axis. The code using atan and atan2 is as follows:

Using atan:

cpp
#include <iostream>
#include <cmath>

int main() {
    double y = 1;
    double x = 0; // x is zero here
    double result = atan(y/x); // This will cause a divide by zero issue
    std::cout << "The angle is: " << result << std::endl;
    return 0;
}

This code will encounter a division by zero issue when executed.

Using atan2:

cpp
#include <iostream>
#include <cmath>

int main() {
    double y = 1;
    double x = 0;
    double result = atan2(y, x); // Correctly handles x = 0
    std::cout << "The angle is: " << result << " radians" << std::endl;
    return 0;
}

This code executes correctly and outputs the angle as π/2 radians.

Therefore, to comprehensively handle angle calculations for coordinate points, especially when the points may lie in various quadrants or the x-axis may be zero, using atan2 is typically a safer and more direct approach.