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

The Math.Acos function returns number in radians in the range 0 to Math.PI. 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)
    {
                                            // radians              degrees 
        Console.WriteLine(Math.Acos(-2));   // NaN
        Console.WriteLine(Math.Acos(-1));   // 3.141592653589793 ->   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.Acos(Math.PI / 4)));  // 0.7853981633974483 -> pi/4 (45deg)
    }
}

 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

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

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