2129. Polar angle of a point

Find the polar angle of the point.

Input. Two integers are given – the decart coordinates of the point that does not coincide with the origin. Input values do not exceed 10000 by the absolute value.

Output. Print one real number – the value of its polar angle in radians in the interval [0; 2π). The answer must be rounded to 6 digits after the decimal point.

Sample input	Sample output
2 3	0.982794

SOLUTION

geometry

Algorithm analysis

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is uniquely determined by two numbers: a polar angle φ (which is also called an azimuth or phase angle) and a polar radius r. The r coordinate is the distance from the point to the center, or pole of the coordinate system, and the φ coordinate is the angle measured counterclockwise from the ray at 0 ° (sometimes called the polar axis of the coordinate system).

Let point P have cartesian coordinates (x, y) and polar coordinates (r, φ). Then the transformation formulas from the polar coordinate system to the cartesian one have the form:

Function atan2(double y, double x) computes the arctangent of y / x in the range (-π; π]. If x = 0, or both parameters are zero, then the function returns 0. In this problem the polar angle should be printed in the interval [0; 2π). To do this, in the case of a negative value of atan2 function, add 2π to the result.

Algorithm realization

Compute the polar angle of a point using function atan2. If the result of atan2 function is negative, then 2π should be added to it, since the answer must be in the interval [0; 2π).

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

res = atan2(b,a);

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

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

Algorithm realization – 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 realization

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 realization

import math

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

res = math.atan2(b,a)

if (res < 0) :

res += 2 * math.pi

print("%.6f" %res)