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C# / .NET - Math.Acos() method example

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Created by:
Dirask Admin - Marvin
1820

The Math.Acos function returns number in radians in the range 0 to Math.PI.Ā Based on this function we are able to calculate the inverted cosine function value.

using System;

public class Program
{
    public static void Main(string[] args) 
    {
        Console.WriteLine(  Math.Acos( -2  )); // NaN
        Console.WriteLine(  Math.Acos( -1  )); // 3.1415926535897930 ->  180
        Console.WriteLine(  Math.Acos( -0.5)); // 2.0943951023931957 -> ~120
        Console.WriteLine(  Math.Acos( 0   )); // 1.5707963267948966 ->   90
        Console.WriteLine(  Math.Acos( 0.5 )); // 1.0471975511965979 ->  ~60
        Console.WriteLine(  Math.Acos( 1   )); // 0                  ->    0
        Console.WriteLine(  Math.Acos( 2   )); // NaN

        Console.WriteLine(  Math.Acos( 0.7071067811865476)); // 0.7853981633974483 -> 45 deg
        Console.WriteLine(  Math.Acos( 0.8660254037844387)); // 0.5235987755982987 -> 30 deg
                            
        Console.WriteLine(  Math.Acos(Math.Cos(Math.PI / 4))); // 0.7853981633974483 -> pi/4 (45deg)
        Console.WriteLine(  Math.Cos( Math.Cos(Math.PI / 4))); // 0.7853981633974483 -> pi/4 (45deg)
    }
}

Ā Another way to look at Acos function:

using System;

public class Program
{
    static double CalculateAngle(double b, double h)
    {
        return Math.Acos(b / h);
    }

    public static void Main(string[] args)
    {
        /*
          |\
          | \ h
        a |  \
          |__*\ <- angle
            b
            
        */

        double a, b, h;

        // a, b and h build isosceles right triangle
        a = 3;
        b = a;
        h = Math.Sqrt(a * a + b * b);
        Console.WriteLine( CalculateAngle(b, h)); // 0.7853981633974483 <-  45 degrees

        // a, b and h build half of equilateral triangle
        a = 3;
        b = a * Math.Sqrt(3);
        h = Math.Sqrt(a * a + b * b);
        Console.WriteLine( CalculateAngle(b, h)); // 0.5235987755982987 <- ~30 degrees

        // a, b and h are not able to build triangle
        a = 3;
        b = a;
        h = 1;
        Console.WriteLine( CalculateAngle(b, h)); // NaN
    }
}

1. Documentation

Syntax
namespace System
{
    public static class Math
    {
        // ...
        public static double Acos(double number) { ... }
        // ...
    }
}
Parameters

number - doubleĀ value that represents the result of the operationĀ adjacent / hypotenuse on the right triangle.

number should be in the range -1 to +1.

Result

number value in radians in the range 0 to Math.PI (primitive value).

If the value can not be calculated NaN is returned.

Description

Acos is a static method that takes only one parameter and returns an approximation of the result of the mathematical function arccosine(x).

2. Working with degrees

using System;

public class Program
{
    static double CalculateAngle(double b, double h)
    {
        double angle = Math.Acos(b / h);

        return (180 / Math.PI) * angle; // rad to deg conversion
    }

    public static void Main(string[] args)
    {
        /*
          |\
          | \ h
        a |  \
          |__*\ <- angle
            b
        */

        double a, b, h;

        // a, b and h build isosceles right triangle
        a = 3;
        b = a;
        h = Math.Sqrt(a * a + b * b);
        Console.WriteLine(  CalculateAngle(b, h) ); // 45 degrees

        // a, b and h build half of equilateral triangle
        a = 3;
        b = a * Math.Sqrt(3);
        h = Math.Sqrt(a * a + b * b);
        Console.WriteLine(  CalculateAngle(b, h) ); // ~30 degrees

        // a, b and h are not able to build triangle
        a = 3;
        b = a;
        h = 1;
        Console.WriteLine(  CalculateAngle(b, h) ); // NaN
    }
}

References

  1. Inverse trigonometric functions - Wikipedia

C# / .NET - Math object

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