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Code Conversion

In the field of mathematics and science, angles are often measured in degrees. However, there are alternative units of measurement for angles, such as radians and milliradians. Radians are a unit of angular measurement that is closely related to the radius of a circle. On the other hand, milliradians (mrad) are even smaller units of angular measurement, where 1 milliradian is equal to 1/1000 of a radian.

The need to convert between different units of angular measurement arises in various applications, including physics, engineering, astronomy, and computer graphics. In this article, we will focus on the conversion of milliradians to degrees using a simple program.

## Problem Statement

Given an angle in milliradians, the task is to convert it to degrees using a predefined formula. The formula involves multiplying the milliradian value by a conversion factor and dividing by π (pi).

## Example

Let's take the example of an angle given in milliradians: 1000.5 mrad.

The formula for conversion is: `degree = (milliradian * 180) / (π * 1000)`

Here, π is a mathematical constant approximately equal to 3.14159.

Plugging in the values:
`degree = (1000.5 * 180) / (3.14159 * 1000) ≈ 57.324427 degrees`

## Idea to Solve

To solve this problem, we need to implement a program that takes a milliradian value as input, applies the conversion formula, and outputs the corresponding angle in degrees. The program should use the defined formula and the mathematical constant π.

## Pseudocode

``````FUNCTION milliradian_to_degree(milliradian)
degree = (milliradian * 180) / (π * 1000)

FUNCTION main()
RETURN 0``````

## Algorithm Explanation

1. Define the function `milliradian_to_degree(milliradian)` that takes a milliradian value as input.
2. Inside the function, calculate the corresponding degree using the formula provided: `degree = (milliradian * 180) / (π * 1000)`.
3. Print the milliradian and degree values using a formatted output.
4. In the `main()` function, call `milliradian_to_degree()` with different milliradian values: 1, 70.8, and 1000.5.

## Program Solution

``````//C Program
#include <stdio.h>

#include <math.h>

//Find the degree of given milliradian
{
// Calculate given milliradian to degree
double degree = (milliradian * 180) / (M_PI * 1000);
//Display result
}
int main()
{
//Simple test
return 0;
}``````

#### Output

``````Milliradian : 1.000000  Degree : 0.057296
Milliradian : 70.800000  Degree : 4.056541
Milliradian : 1000.500000  Degree : 57.324427``````
``````/*
C++ program
*/
#include<iostream>
#include<math.h>
using namespace std;
class MyMath
{
public:
//Find the degree of given milliradian
{
// Calculate given milliradian to degree
double degree = (milliradian * 180) / (M_PI * 1000);
cout << "Milliradian : " << milliradian << " Degree : " << degree << "\n";
}
};
int main()
{
MyMath obj =  MyMath();
//Simple test
return 0;
}``````

#### Output

``````Milliradian : 1 Degree : 0.0572958
Milliradian : 70.8 Degree : 4.05654
Milliradian : 1000.5 Degree : 57.3244``````
``````/*
Java program
*/
class MyMath
{
//Find the degree of given milliradian
{
// Calculate given milliradian to degree
double degree = (milliradian * 180) / (Math.PI * 1000);
System.out.print("Milliradian : " + milliradian + " Degree : " + degree + "\n");
}
public static void main(String[] args)
{
MyMath obj = new MyMath();
//Simple test
}
}``````

#### Output

``````Milliradian : 1.0 Degree : 0.057295779513082325
Milliradian : 70.8 Degree : 4.056541189526229
Milliradian : 1000.5 Degree : 57.324427402838865``````
``````/*
C# program
*/
using System;
class MyMath
{
//Find the degree of given milliradian
{
// Calculate given milliradian to degree
double degree = (milliradian * 180) / (Math.PI * 1000);
Console.Write("Milliradian : " + milliradian + " Degree : " + degree + "\n");
}
public static void Main(String[] args)
{
MyMath obj = new MyMath();
//Simple test
}
}``````

#### Output

``````Milliradian : 1 Degree : 0.0572957795130823
Milliradian : 70.8 Degree : 4.05654118952623
Milliradian : 1000.5 Degree : 57.3244274028389``````
``````<?php
/*
Php program
*/
class MyMath
{
//Find the degree of given milliradian
{
// Calculate given milliradian to degree
\$degree = (\$milliradian * 180) / (M_PI * 1000);
}
}

function main()
{
\$obj = new MyMath();
//Simple test
}
main();``````

#### Output

``````Milliradian : 1 Degree : 0.057295779513082
Milliradian : 70.8 Degree : 4.0565411895262
Milliradian : 1000.5 Degree : 57.324427402839``````
``````/*
Node Js program
*/
class MyMath
{
//Find the degree of given milliradian
{
// Calculate given milliradian to degree
var degree = (milliradian * 180) / (Math.PI * 1000);
process.stdout.write("Milliradian : " + milliradian + " Degree : " + degree + "\n");
}
}

function main()
{
var obj = new MyMath();
//Simple test
}
main();``````

#### Output

``````Milliradian : 1 Degree : 0.057295779513082325
Milliradian : 70.8 Degree : 4.056541189526229
Milliradian : 1000.5 Degree : 57.324427402838865``````
``````#   Python 3 program
import math

class MyMath :
# Find the degree of given milliradian
#  Calculate given milliradian to degree
degree = (milliradian * 180) / (math.pi * 1000)
print("Milliradian : ", milliradian ," Degree : ", degree ,"\n", end = "")

def main() :
obj = MyMath()
# Simple test

if __name__ == "__main__": main()``````

#### Output

``````Milliradian :  1  Degree :  0.057295779513082325
Milliradian :  70.8  Degree :  4.056541189526229
Milliradian :  1000.5  Degree :  57.324427402838865``````
``````#   Ruby program

class MyMath

# Find the degree of given milliradian

#  Calculate given milliradian to degree
degree = (milliradian * 180) / (Math::PI * 1000)
end
end
def main()

obj = MyMath.new()
# Simple test
end
main()``````

#### Output

``````Milliradian : 1 Degree : 0.057295779513082325
Milliradian : 70.8 Degree : 4.056541189526229
Milliradian : 1000.5 Degree : 57.324427402838865
``````
``````/*
Scala program
*/
class MyMath
{
//Find the degree of given milliradian
// Calculate given milliradian to degree
var degree: Double = (milliradian * 180) / (Math.PI * 1000);
print("Milliradian : " + milliradian + " Degree : " + degree + "\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: MyMath = new MyMath();
//Simple test
}
}``````

#### Output

``````Milliradian : 1.0 Degree : 0.057295779513082325
Milliradian : 70.8 Degree : 4.056541189526229
Milliradian : 1000.5 Degree : 57.324427402838865``````
``````/*
Swift program
*/

import Foundation

class MyMath
{
//Find the degree of given milliradian
{
// Calculate given milliradian to degree
let degree: Double = (milliradian * 180) / (Double.pi * 1000);
print("Milliradian : ", milliradian ," Degree : ", degree ,"\n", terminator: "");
}
}
func main()
{
let obj: MyMath = MyMath();
//Simple test
}
main();``````

#### Output

``````Milliradian :  1.0  Degree :  0.0572957795130823
Milliradian :  70.8  Degree :  4.05654118952623
Milliradian :  1000.5  Degree :  57.3244274028389``````

## Time Complexity

The time complexity of this program is constant for each conversion. The calculations involved are basic arithmetic operations, which are generally executed in constant time on modern computers. Therefore, the time complexity can be considered O(1), indicating constant time complexity.

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