Convert gradian to radian
Angular measurement systems play a vital role in mathematics, physics, and engineering. One such system is gradians, which divides a right angle into 100 units. Radians, on the other hand, are a more fundamental angular measurement used extensively in mathematics and physics. Converting angles from gradians to radians is an important task that involves understanding these measurement systems and the relationships between them.
Problem Statement and Description
The task is to convert an angle given in gradians to its equivalent value in radians. Radians are a unit of angular
measurement that relates the angle to the length of the radius of a circle. The formula to convert from gradians to
radians is (gradian * π) / 200
, where π (pi) is a mathematical constant approximately equal to 3.14159.
This formula takes the given angle in gradians, multiplies it by π, and then divides by 200 to obtain the equivalent
angle in radians.
Example
Let's take an example to illustrate the problem. Suppose we have an angle of 60 gradians that we want to convert to radians. Using the formula:
Radian = (Gradian * π) / 200
Radian = (60 * π) / 200
Radian ≈ 0.94248
So, 60 gradians is approximately equal to 0.94248 radians.
Idea to Solve the Problem
To solve this problem, we need to create a program that takes an angle in gradians as input, applies the conversion formula, and then outputs the equivalent angle in radians. We will use a function to perform this conversion, and the main program will call this function for different test cases.
Pseudocode
Here's the pseudocode for the program:
function gradian_to_radian(gradian):
radian = (gradian * π) / 200
return radian
Algorithm Explanation
- Define the
gradian_to_radian
function that takes a parametergradian
. - Inside the function, calculate the equivalent radian using the formula
(gradian * π) / 200
. - Return the calculated radian.
- In the
main
program, call thegradian_to_radian
function with different test cases: 1, 50.80, and 70.50. - Print the results.
Program Solution
//C Program
//Convert gradian to radian
#include <stdio.h>
#include <math.h>
//Find the radian of given gradian
void gradian_to_radian(double gradian)
{
// Formula : (gradian*π)/200
// Calculate given gradian to radian
double radian = (gradian * M_PI) / 200;
//Display result
printf("Gradian : %lf radian : %lf\n", gradian, radian);
}
int main()
{
//Simple test
gradian_to_radian(1);
gradian_to_radian(50.80);
gradian_to_radian(70.50);
return 0;
}
Output
Gradian : 1.000000 radian : 0.015708
Gradian : 50.800000 radian : 0.797965
Gradian : 70.500000 radian : 1.107411
/*
Java program
Convert gradian to radian
*/
class MyMath
{
//Find the radian of given gradian
public void gradian_to_radian(double gradian)
{
// Formula : (gradian*π)/200
// Calculate given gradian to radian
double radian = (gradian * Math.PI) / 200;
System.out.print("Gradian : " + gradian + " radian : " + radian + "\n");
}
public static void main(String[] args)
{
MyMath obj = new MyMath();
//Simple test
obj.gradian_to_radian(1);
obj.gradian_to_radian(50.80);
obj.gradian_to_radian(70.50);
}
}
Output
Gradian : 1.0 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402
/*
C++ program
Convert gradian to radian
*/
#include<iostream>
#include<math.h>
using namespace std;
class MyMath
{
public:
//Find the radian of given gradian
void gradian_to_radian(double gradian)
{
// Formula : (gradian*π)/200
// Calculate given gradian to radian
double radian = (gradian * M_PI) / 200;
cout << "Gradian : " << gradian << " radian : " << radian << "\n";
}
};
int main()
{
MyMath obj = MyMath();
//Simple test
obj.gradian_to_radian(1);
obj.gradian_to_radian(50.80);
obj.gradian_to_radian(70.50);
return 0;
}
Output
Gradian : 1 radian : 0.015708
Gradian : 50.8 radian : 0.797965
Gradian : 70.5 radian : 1.10741
/*
C# program
Convert gradian to radian
*/
using System;
class MyMath
{
//Find the radian of given gradian
public void gradian_to_radian(double gradian)
{
// Formula : (gradian*π)/200
// Calculate given gradian to radian
double radian = (gradian * Math.PI) / 200;
Console.Write("Gradian : " + gradian + " radian : " + radian + "\n");
}
public static void Main(String[] args)
{
MyMath obj = new MyMath();
//Simple test
obj.gradian_to_radian(1);
obj.gradian_to_radian(50.80);
obj.gradian_to_radian(70.50);
}
}
Output
Gradian : 1 radian : 0.015707963267949
Gradian : 50.8 radian : 0.797964534011807
Gradian : 70.5 radian : 1.1074114103904
<?php
/*
Php program
Convert gradian to radian
*/
class MyMath
{
//Find the radian of given gradian
public function gradian_to_radian($gradian)
{
// Formula : (gradian*π)/200
// Calculate given gradian to radian
$radian = ($gradian * M_PI) / 200;
echo "Gradian : ". $gradian ." radian : ". $radian ."\n";
}
}
function main()
{
$obj = new MyMath();
//Simple test
$obj->gradian_to_radian(1);
$obj->gradian_to_radian(50.80);
$obj->gradian_to_radian(70.50);
}
main();
Output
Gradian : 1 radian : 0.015707963267949
Gradian : 50.8 radian : 0.79796453401181
Gradian : 70.5 radian : 1.1074114103904
/*
Node Js program
Convert gradian to radian
*/
class MyMath
{
//Find the radian of given gradian
gradian_to_radian(gradian)
{
// Formula : (gradian*π)/200
// Calculate given gradian to radian
var radian = (gradian * Math.PI) / 200;
process.stdout.write("Gradian : " + gradian + " radian : " + radian + "\n");
}
}
function main()
{
var obj = new MyMath();
//Simple test
obj.gradian_to_radian(1);
obj.gradian_to_radian(50.80);
obj.gradian_to_radian(70.50);
}
main();
Output
Gradian : 1 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402
# Python 3 program
# Convert gradian to radian
import math
class MyMath :
# Find the radian of given gradian
def gradian_to_radian(self, gradian) :
# Formula : (gradian*π)/200
# Calculate given gradian to radian
radian = (gradian * math.pi) / 200
print("Gradian : ", gradian ," radian : ", radian ,"\n", end = "")
def main() :
obj = MyMath()
# Simple test
obj.gradian_to_radian(1)
obj.gradian_to_radian(50.80)
obj.gradian_to_radian(70.50)
if __name__ == "__main__": main()
Output
Gradian : 1 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402
# Ruby program
# Convert gradian to radian
class MyMath
# Find the radian of given gradian
def gradian_to_radian(gradian)
# Formula : (gradian*π)/200
# Calculate given gradian to radian
radian = (gradian * Math::PI) / 200
print("Gradian : ", gradian ," radian : ", radian ,"\n")
end
end
def main()
obj = MyMath.new()
# Simple test
obj.gradian_to_radian(1)
obj.gradian_to_radian(50.80)
obj.gradian_to_radian(70.50)
end
main()
Output
Gradian : 1 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402
/*
Scala program
Convert gradian to radian
*/
class MyMath
{
//Find the radian of given gradian
def gradian_to_radian(gradian: Double): Unit = {
// Formula : (gradian*π)/200
// Calculate given gradian to radian
var radian: Double = (gradian * Math.PI) / 200;
print("Gradian : " + gradian + " radian : " + radian + "\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: MyMath = new MyMath();
//Simple test
obj.gradian_to_radian(1);
obj.gradian_to_radian(50.80);
obj.gradian_to_radian(70.50);
}
}
Output
Gradian : 1.0 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402
/*
Swift program
Convert gradian to radian
*/
import Foundation
class MyMath
{
//Find the radian of given gradian
func gradian_to_radian(_ gradian: Double)
{
// Formula : (gradian*π)/200
// Calculate given gradian to radian
let radian: Double = (gradian * Double.pi) / 200;
print("Gradian : ", gradian ," radian : ", radian ,"\n", terminator: "");
}
}
func main()
{
let obj: MyMath = MyMath();
//Simple test
obj.gradian_to_radian(1);
obj.gradian_to_radian(50.80);
obj.gradian_to_radian(70.50);
}
main();
Output
Gradian : 1.0 radian : 0.015707963267949
Gradian : 50.8 radian : 0.797964534011807
Gradian : 70.5 radian : 1.1074114103904
Time Complexity
Similar to the previous problem, the time complexity of this program is constant for each conversion. It involves basic arithmetic operations like multiplication and division, and the number of operations remains consistent regardless of the input gradians. Thus, the time complexity is O(1).
Please share your knowledge to improve code and content standard. Also submit your doubts, and test case. We improve by your feedback. We will try to resolve your query as soon as possible.
New Comment