Polar to Rectangular conversion in C++

By Dinesh Kumar

In this tutorial, we are going to learn Polar to Rectangular conversion in C++. Here we will learn about the rectangular form, polar form, and Polar to Rectangular conversion. After that, we will see the C++ program for the same.

Let us see how to represent z=a+ib in polar form:-

As, shown in the figure:
r ² = a ² + b ² (Pythagoras theorem)

By using the basic trigonometry:

=> cosθ=a/r and sinθ=b/r

=> a=rcosθ  and b=rsinθ

Substitute the values of a and b in z=a+ib, we get
z=a+bi =rcosθ+(rsinθ)i =r(cosθ+isinθ)
This is called as polar form.

Conversion of polar form to rectangular form in C++

To convert polar form to rectangular form i.e.
r(cosθ+isinθ) to a+ib
we have to calculate the value of a and b:-
a = r cos θ

b = r sin θ

and substitute these values in a+ib to get the rectangular form.

C++ program

So, here is the C++ implementation of the above conversion:-

#include<bits/stdc++.h>
using namespace std; 

/*===============================================
FUNCTION FOR CONVERSION FROM POLAR TO RECTANGULAR
================================================*/
void convert_to_rect(int r, int angle)
{
    int a,b;
    //Calculating values of a and b
    a=r*cos(angle);
    b=r*sin(angle);
    //Displaying rectangular form
    cout<<"Rectangular form is: "<<a<<" + i("<<b<<")"<<endl;

}

/*======================================
   MAIN FUNCTION
=======================================*/
int main() 
{ 
    //Initializing r and angle(in radian)
    int r,angle;
    r=5;
    angle=10;
    //Displaying Polar form
    cout<<"Polar form is: "<<r<<"*(cos("<<angle<<")+isin("
        <<angle<<"))"<<endl;
    //Passing r and angle to convert_to_rect function 
    convert_to_rect(r,angle); 
    return 0; 
} 

Output:-

Polar form is: 5*(cos(10)+isin(10))
Rectangular form is: -4 + i(-2)

Also read: Convert cartesian to polar coordinates in C++