Polar to Rectangular conversion in C++
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)
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