2129. Polar angle of a point

Find the polar angle of the given point.

Input. Two integers are given – the Cartesian coordinates of a point that does not coincide with the origin. The absolute value of each number does not exceed 10000.

Output. Print one real number – the polar angle of the given point in radians from the interval [0; 2π). The answer should be rounded to 6 decimal places.

Sample input	Sample output
2 3	0.982794

SOLUTION

geometry

Algorithm analysis

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:

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

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

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;

}

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();

}

}

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 2π to it, since the angle must lie within the interval [0; 2π).

if (res < 0) :

res += 2 * math.pi

Print the answer.

print("%.6f" %res)