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Program to convert polar co-ordinates to equivalent cartesian co-ordinates
  • Last Updated : 08 Mar, 2021

Given two integers r and θ (in degree) representing polar coordinates of a point (r, θ), the task is to find the Cartesian coordinates of the given point.

Examples:

Input: r = 1.4142, θ = 45
Output: 1.000, 1.000

Input: r = 3, θ = 30
Output: 2.598, 1.500

Approach: Let the cartesian coordinates of the point be (x, y). The polar coordinates and the Cartesian coordinates can be related using the following equations:



x = r*cosθ and y = r*sinθ

Follow the steps below to solve the problem:

  • Convert θ from degrees to radian as θ(in radian) = θ (in degrees) * (3.14159 / 180).
  • Store the x and y coordinate in a variable X and Y respectively.
  • Apply transformation formula and update the value of X = r * cosθ and Y = r * sinθ.
  • Print the value of X and Y as the result.

Below is the implementation of the above approach:

C++14




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to convert degree to radian
double ConvertDegToRad(double degree)
{
    double pi = 3.14159;
    return (degree * (pi / 180.0));
}
 
// Function to convert the polar
// cordinate to cartesian
void ConvertToCartesian(
    pair<double, double> polar)
{
 
    // Convert degerees to radian
    polar.second = ConvertDegToRad(
        polar.second);
 
    // Applying the formula:
    // x = rcos(theata), y = rsin(theta)
    pair<double, double> cartesian
        = { polar.first * cos(polar.second),
            polar.first * sin(polar.second) };
 
    // Print cartesian coordinates
    printf("%0.3f, %0.3f",
           cartesian.first,
           cartesian.second);
}
 
// Driver Code
int main()
{
    // Given polar coordinates
    pair<double,
         double>
        polar = { 1.4142, 45 };
 
    // Function to convert polar
    // coordinates to equivalent
    // cartesian coordinates
    ConvertToCartesian(polar);
 
    return 0;
}

Java




// Java code of above approach
import java.util.*;
 
class GFG
{
 
  // Function to convert degree to radian
  static double ConvertDegToRad(double degree)
  {
    double pi = 3.14159;
    return (degree * (pi / 180.0));
  }
 
  // Function to convert the polar
  // cordinate to cartesian
  static void ConvertToCartesian(
    double[] polar)
  {
 
    // Convert degerees to radian
    polar[1] = ConvertDegToRad(
      polar[1]);
 
    // Applying the formula:
    // x = rcos(theata), y = rsin(theta)
    double[] cartesian
      = { polar[0] * Math.cos(polar[1]),
         polar[0] * Math.sin(polar[1]) };
 
    // Print cartesian coordinates
    System.out.print(String.format("%.3f", cartesian[0])+" "+String.format("%.3f", cartesian[1]));
 
  }
 
  // Driver code
  public static void main(String[] args)
  {
    // Given polar coordinates
 
    double[] polar = { 1.4142, 45 };
 
    // Function to convert polar
    // coordinates to equivalent
    // cartesian coordinates
    ConvertToCartesian(polar);
 
  }
}
 
// This code is contributed by offbeat

Python3




# Python 3 program for the above approach
import math
 
# Function to convert degree to radian
def ConvertDegToRad(degree):
    pi = 3.14159
    return (degree * (pi / 180.0))
 
# Function to convert the polar
# cordinate to cartesian
def ConvertToCartesian(polar):
 
    # Convert degerees to radian
    polar[1] = ConvertDegToRad(polar[1])
 
    # Applying the formula:
    # x = rcos(theata), y = rsin(theta)
    cartesian = [polar[0] * math.cos(polar[1]),
                 polar[0] * math.sin(polar[1])]
 
    # Print cartesian coordinates
    print('%.3f' % cartesian[0],
          '%.3f' % cartesian[1])
 
# Driver Code
if __name__ == "__main__":
 
    # Given polar coordinates
    polar = [1.4142, 45]
 
    # Function to convert polar
    # coordinates to equivalent
    # cartesian coordinates
    ConvertToCartesian(polar)
 
    # This code is contributed by chitranayal.
Output: 
1.000, 1.000

 

Time Complexity: O(1)
Auxiliary Space: O(1)

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