// While the domain of arctangent is all the
// real numbers, the range is only from 
// -pi/2 to pi/2, excluding the end-points,
// as tan(pi/2) and tan(-pi/2) are undefined.
// Additionally, however, this is because y/x is
// equal to (-y)/(-x), and therefore from the
// quotient alone it is impossible to determine
// whether 'x' and 'y' were both positive or both
// negative. In the image below, if the point
// in the first quadrant has an angle of θ,
// then the point in third quadrant has an
// angle of θ - π. We subtract because we want
// the angle to be in (-π, π]:
//
//               |     *
//               |    /:
//               |   / :
//               |  /  : y
//               | /   :
//           -x  |/ θ  :
// --------------+-----*--------
//         :    /|  x
//         :   / |
//      -y :  /  |
//         : /   | For positive slopes,
//         :/    |    0 < θ < π/2
//         *     |
//                       -1
// You will note that tan   does give the angle
// corresponding to the slope of the extended
// line, but this angle is always between
// -π/2 and π/2:
//
//               |
//           *   | For negative slopes,
//           |\  |    -π/2 < θ < 0
//        -y | \ |
//           |  \| x
// --------------+-----*--------
//            -x |\θ :
//               | \ : y
//               |  \:
//               |   *
//               |
//
// If x = 0 and y = 0, then we simply define
// the "angle" to be 0 radians.
//
// Otherwise, we must be careful about dividing
// by zero, so if 'x' is zero, the sign of 'y'
// determines whether we return 'pi/2' or '-pi/2'.
//
// Otherwise, if 'y' is zero, we return 0 or 'pi',
// depending on the sign of 'x'.
//  - While we could also legitimately return
//    '-pi' for x < 0, by convention the range
//    is (-pi, pi].
//                            -1
// Otherwise, we calculate tan  (y/x) and then
// if the coordinate (x, y) is in the second
// or third quadrant, we must add or subtract
// 'pi' to the result returned by 'atan', 
// respectively.

#include <iostream>
#include <cmath>
#include <numbers>

// Function declarations
int main();

// Function definitions
int main() {
    double x{};
    std::cout << "Enter the x-coordinate: ";
    std::cin  >> x;

    double y{};
    std::cout << "Enter the y-coordinate: ";
    std::cin  >> y;

    // The local variable 'pi' is initialized
    // with the value 3.141592653589793
    double pi{ std::numbers::pi };

    if ( x == 0.0 ) {
    } else {
        //        -1 / y \
        // θ = tan  | --- |
        //           \ x /
        double theta{ std::atan( y/x ) };

    }

    return 0;
}