Polar angle of a point#2129

Polar angle of a point (Editorial)

The polar coordinate system is a two-dimensional system in which every point on the plane is uniquely determined by two numbers: the polar radius $r$ and the polar angle $φ$ (also called the azimuth or the phase angle).

The radius $r$ is the distance from the point to the center, or pole, of the coordinate system. The angle $φ$ is the angle between the polar axis and the ray connecting the pole with the point; it is measured counterclockwise from the ray corresponding to the direction of $0°$ (this ray is called the polar axis).

Let point $P$ have Cartesian coordinates $(x, y)$ and polar coordinates $(r, φ)$ . Then the formulas for converting from polar coordinates to Cartesian coordinates are as follows:

{x = r cos φ, y = r sin φ .

\begin{cases} x = r \cos \varphi, \\ y = r \sin \varphi. \end{cases}

The function atan2(double $y$ , double $x$ ) computes the arctangent of $y / x$ and returns an angle in the interval $(- π; π]$ (-\pi; \pi]. If $x = 0$ x = 0 or both arguments are zero, the function returns $0$ .

In this problem, the polar angle must be given in the interval $[0; 2 π)$ [0; 2\pi). Therefore, if the result of atan2 is negative, you should add $2 π$ to it.

Algorithm implementation

Read the input data.

scanf("%lf %lf",&a,&b);

The polar angle of a point is computed using the atan2 function.

res = atan2(b,a);

If the result of atan2 is negative, you should add $2 π$ to it, since the angle must lie within the interval $[0; 2 π)$ [0; 2\pi).

if (res < 0) res += 2*PI;

Print the answer.

printf("%.6lf\n",res);

Algorithm implementation – class

#include <stdio.h>
#include <math.h>
#define PI acos(-1.0)

class Point
{
private:
  double x, y;
public:
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  void ReadPoint(void)
  {
    scanf("%lf %lf",&x,&y);
  }
  double GetPolarAngle()
  {
    double res = atan2(y,x);
    if (res < 0) res += 2*PI;
    return res;
  }
};

int main(void)
{
  Point p;
  p.ReadPoint();
  printf("%.6lf\n",p.GetPolarAngle());
  return 0;
}

C++

Java implementation

import java.util.*;

public class Main
{
  public static void main(String[] args)
  {
    Scanner con = new Scanner(System.in);
    double a = con.nextDouble();
    double b = con.nextDouble();
    
    double res = Math.atan2(b,a);
    if (res < 0) res += 2 * Math.PI;
    System.out.println(res);
    con.close();
  }
}

Java

Python implementation

Read the input data.

import math
a, b = map(float,input().split())

The polar angle of a point is computed using the atan2 function.

res = math.atan2(b,a)

If the result of atan2 is negative, you should add $2 π$ to it, since the angle must lie within the interval $[0; 2 π)$ [0; 2\pi).

if (res < 0) :
  res += 2 * math.pi

Print the answer.

print("%.6f" %res)