Question

Write procedures using c++ for converting between rectangular and polar coordinates named xy2polar and polar2xy. Invoking xy2polar(x,y,r,t) should take the rectangular coordinates (x,y) and save the resulting polar coordinates; (r,theta) are r and t, respectively. The procedure polar2xy(r,t,x,y) should have the reverse effect.

Be sure to handle the origin in a sensible manner.

It is useful to explore the following C++ procedures, which are housed in the cmath header file:

Variants of the absolute value function

• int abs(int x)

• long labs(long x)

• double fabs(double x)

Other interesting/needed procedures

• sin

• cos

• tan

• asin

• acos

• atan

• ceil

• floor

• hypot: Computes the hypotenuse of triangle with legs x and y

• sqrt

My intention is for you to use intuition to determine what these procedures do. However, you may either write a quick main() procedure to check, ask the instructor, or even Google them.

Answer 1

// C++ program to convert from polar to rectangular and vice versa

#include <iostream>

#include <cmath>

using namespace std;

// function declaration

void xy2polar(double x, double y, double &r, double &t);

void polar2xy(double r, double t, double &x, double &y);

int main() {

       double x,y,r,t;

       cout<<"Enter x and y (with space): ";

       cin>>x>>y;

       xy2polar(x,y,r,t);

       cout<<"Radius : "<<r<<" Theta : "<<t<<" radians"<<endl;

       cout<<"Enter radius and theta (with space) : ";

       cin>>r>>t;

       polar2xy(r,t,x,y);

       cout<<"X : "<<x<<" Y : "<<y<<endl;

       return 0;

}

// function to convert rectangular coordinates to polar form

void xy2polar(double x, double y, double &r, double &t)

{

       r = (sqrt(x*x + y*y));

       if(x == 0 && y == 0)

             t = 0;

       else

       {

             t = atan(y/x);

             // if point is in Quadrant 2 or 3 add 180 degrees

             if((x<0 && y>=0) || (x < 0 && y < 0))

                    t += atan(1)*4;

             // if point is in Quadrant 4 add 360 degrees

             else if(x >= 0 && y<0)

                    t += atan(1)*8;

       }

}

// function to convert polar form to rectangular coordinate

void polar2xy(double r, double t, double &x, double &y)

{

       x = r*cos(t);

       y = r*sin(t);

}

//end of program

Output: