Given two integers r and ? (in degree) representing polar coordinates of a point (r, ?), the task is to find the Cartesian coordinates of the given point.
Examples:
Input: r = 1.4142, ? = 45
Output: 1.000, 1.000Input: r = 3, ? = 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*cos? and y = r*sin?
Follow the steps below to solve the problem:
- Convert ? from degrees to radian as ?(in radian) = ? (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 * cos? and Y = r * sin?.
- 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 radiandouble ConvertDegToRad(double degree){ double pi = 3.14159; return (degree * (pi / 180.0));}// Function to convert the polar// coordinate to cartesianvoid ConvertToCartesian( pair<double, double> polar){ // Convert degrees to radian polar.second = ConvertDegToRad( polar.second); // Applying the formula: // x = rcos(theta), 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 Codeint 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 approachimport 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 // coordinate to cartesian static void ConvertToCartesian( double[] polar) { // Convert degrees to radian polar[1] = ConvertDegToRad( polar[1]); // Applying the formula: // x = rcos(theta), 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 approachimport math# Function to convert degree to radiandef ConvertDegToRad(degree): pi = 3.14159 return (degree * (pi / 180.0))# Function to convert the polar# coordinate to cartesiandef ConvertToCartesian(polar): # Convert degrees to radian polar[1] = ConvertDegToRad(polar[1]) # Applying the formula: # x = rcos(theta), 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 Codeif __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. |
C#
// C# program for the above approachusing System;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 // coordinate to cartesian static void ConvertToCartesian( Double[] polar) { // Convert degrees to radian polar[1] = ConvertDegToRad( polar[1]); // Applying the formula: // x = rCos(theta), y = rSin(theta) Double[] cartesian = { polar[0] * Math.Cos(polar[1]), polar[0] * Math.Sin(polar[1]) }; // Print cartesian coordinates Console.Write(String.Format("{0:0.000}", cartesian[0])+ ", "+String.Format("{0:0.000}", cartesian[1])); } // Driver code public static void Main() { // Given polar coordinates Double[] polar = { 1.4142, 45 }; // Function to convert polar // coordinates to equivalent // cartesian coordinates ConvertToCartesian(polar); }}// This code is contributed by Shubham Singh |
Javascript
<script>// JavaScript code of above approach// Function to convert degree to radianfunction ConvertDegToRad(degree){ let pi = 3.14159; return (degree * (pi / 180.0));}// Function to convert the polar // coordinate to cartesianfunction ConvertToCartesian(polar){ // Convert degrees to radian polar[1] = ConvertDegToRad( polar[1]); // Applying the formula: // x = rcos(theta), y = rsin(theta) let cartesian = [ polar[0] * Math.cos(polar[1]), polar[0] * Math.sin(polar[1]) ]; // Print cartesian coordinates document.write((cartesian[0]).toFixed(3)+", " +(cartesian[1]).toFixed(3));}// Driver codelet polar=[1.4142, 45 ];// Function to convert polar// coordinates to equivalent// cartesian coordinatesConvertToCartesian(polar);// This code is contributed by avanitrachhadiya2155</script> |
Output:
1.000, 1.000
Time Complexity: O(1)
Auxiliary Space: O(1)
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