MathF.Atanh() Method in C# with Examples

The MathF.Atanh() method in C# returns the hyperbolic arc-tangent of a single-precision floating-point value. The hyperbolic arc-tangent is the inverse of the hyperbolic tangent function and is defined only for values in the range (-1, 1).

For values outside this range, the method returns NaN (Not a Number). The method is useful in mathematical calculations involving hyperbolic functions and inverse transformations.

Syntax

Following is the syntax −

public static float Atanh(float val);

Parameters

• val − A single-precision floating-point number representing the hyperbolic tangent whose inverse is to be found. Must be in the range (-1, 1).

Return Value

The method returns a float representing the hyperbolic arc-tangent of the input value. Returns NaN if the input is outside the valid range (-1, 1).

Using MathF.Atanh() with Valid Range

Example

using System;

public class Demo {
   public static void Main() {
      float val1 = 0.5f;
      float val2 = -0.8f;
      float val3 = 0.0f;
      
      Console.WriteLine("Atanh(0.5) = " + MathF.Atanh(val1));
      Console.WriteLine("Atanh(-0.8) = " + MathF.Atanh(val2));
      Console.WriteLine("Atanh(0.0) = " + MathF.Atanh(val3));
   }
}

The output of the above code is −

Atanh(0.5) = 0.5493061
Atanh(-0.8) = -1.0986123
Atanh(0.0) = 0

Using MathF.Atanh() with Invalid Range

Example

using System;

public class Demo {
   public static void Main() {
      float val1 = 25f;
      float val2 = -15f;
      float val3 = 1.0f;
      float val4 = -1.0f;
      
      Console.WriteLine("Atanh(25) = " + MathF.Atanh(val1));
      Console.WriteLine("Atanh(-15) = " + MathF.Atanh(val2));
      Console.WriteLine("Atanh(1.0) = " + MathF.Atanh(val3));
      Console.WriteLine("Atanh(-1.0) = " + MathF.Atanh(val4));
   }
}

The output of the above code is −

Atanh(25) = NaN
Atanh(-15) = NaN
Atanh(1.0) = ?
Atanh(-1.0) = -?

Common Use Cases

Example

using System;

public class Demo {
   public static void Main() {
      // Demonstrating relationship between Tanh and Atanh
      float original = 0.7f;
      float hyperbolicTangent = MathF.Tanh(original);
      float inverseResult = MathF.Atanh(hyperbolicTangent);
      
      Console.WriteLine("Original value: " + original);
      Console.WriteLine("Tanh(" + original + ") = " + hyperbolicTangent);
      Console.WriteLine("Atanh(" + hyperbolicTangent + ") = " + inverseResult);
      Console.WriteLine("Values match: " + Math.Abs(original - inverseResult) < 0.0001f);
   }
}

The output of the above code is −

Original value: 0.7
Tanh(0.7) = 0.6043677
Atanh(0.6043677) = 0.7000001
Values match: True

Conclusion

The MathF.Atanh() method calculates the hyperbolic arc-tangent of single-precision floating-point values. It only accepts values in the range (-1, 1), returning NaN for values outside this range and infinity for boundary values ±1.