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

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Created by:

Mohammad-Oneal

327

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.

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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:

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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

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Syntax	xxxxxxxxxx 1 namespace System 2 { 3 public static class Math 4 { 5 // ... 6 public static double Acos(double number) { ... } 7 // ... 8 } 9 }
Parameters	`number` - double value that represents the result of the operation `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

Edit

xxxxxxxxxx
 
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
    }
}