Math::Tanh Method (Double)

// Example for the hyperbolic Math::Tanh( double ) method.
using namespace System;

// Evaluate hyperbolic identities with a given argument.
void UseTanh( double arg )
{
   double tanhArg = Math::Tanh( arg );

   // Evaluate tanh(X) == sinh(X) / cosh(X).
   Console::WriteLine( "\n                        Math::Tanh({0}) == {1:E16}\n"
   "      Math::Sinh({0}) / Math::Cosh({0}) == {2:E16}", arg, tanhArg, (Math::Sinh( arg ) / Math::Cosh( arg )) );

   // Evaluate tanh(2 * X) == 2 * tanh(X) / (1 + tanh^2(X)).
   Console::WriteLine( "                    2 * Math::Tanh({0}) /", arg, 2.0 * tanhArg );
   Console::WriteLine( "              (1 + (Math::Tanh({0}))^2) == {1:E16}", arg, 2.0 * tanhArg / (1.0 + tanhArg * tanhArg) );
   Console::WriteLine( "                        Math::Tanh({0}) == {1:E16}", 2.0 * arg, Math::Tanh( 2.0 * arg ) );
}


// Evaluate a hyperbolic identity that is a function of two arguments.
void UseTwoArgs( double argX, double argY )
{

   // Evaluate tanh(X + Y) == (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y)).
   Console::WriteLine( "\n    (Math::Tanh({0}) + Math::Tanh({1})) /\n"
   "(1 + Math::Tanh({0}) * Math::Tanh({1})) == {2:E16}", argX, argY, (Math::Tanh( argX ) + Math::Tanh( argY )) / (1.0 + Math::Tanh( argX ) * Math::Tanh( argY )) );
   Console::WriteLine( "                        Math::Tanh({0}) == {1:E16}", argX + argY, Math::Tanh( argX + argY ) );
}

int main()
{
   Console::WriteLine( "This example of hyperbolic Math::Tanh( double )\n"
   "generates the following output." );
   Console::WriteLine( "\nEvaluate these hyperbolic identities "
   "with selected values for X:" );
   Console::WriteLine( "   tanh(X) == sinh(X) / cosh(X)" );
   Console::WriteLine( "   tanh(2 * X) == 2 * tanh(X) / (1 + tanh^2(X))" );
   UseTanh( 0.1 );
   UseTanh( 1.2 );
   UseTanh( 4.9 );
   Console::WriteLine( "\nEvaluate [tanh(X + Y) == "
   "(tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y))]"
   "\nwith selected values for X and Y:" );
   UseTwoArgs( 0.1, 1.2 );
   UseTwoArgs( 1.2, 4.9 );
}

/*
This example of hyperbolic Math::Tanh( double )
generates the following output.

Evaluate these hyperbolic identities with selected values for X:
   tanh(X) == sinh(X) / cosh(X)
   tanh(2 * X) == 2 * tanh(X) / (1 + tanh^2(X))

                        Math::Tanh(0.1) == 9.9667994624955819E-002
      Math::Sinh(0.1) / Math::Cosh(0.1) == 9.9667994624955819E-002
                    2 * Math::Tanh(0.1) /
              (1 + (Math::Tanh(0.1))^2) == 1.9737532022490401E-001
                        Math::Tanh(0.2) == 1.9737532022490401E-001

                        Math::Tanh(1.2) == 8.3365460701215521E-001
      Math::Sinh(1.2) / Math::Cosh(1.2) == 8.3365460701215521E-001
                    2 * Math::Tanh(1.2) /
              (1 + (Math::Tanh(1.2))^2) == 9.8367485769368024E-001
                        Math::Tanh(2.4) == 9.8367485769368024E-001

                        Math::Tanh(4.9) == 9.9988910295055444E-001
      Math::Sinh(4.9) / Math::Cosh(4.9) == 9.9988910295055433E-001
                    2 * Math::Tanh(4.9) /
              (1 + (Math::Tanh(4.9))^2) == 9.9999999385024030E-001
                        Math::Tanh(9.8) == 9.9999999385024030E-001

Evaluate [tanh(X + Y) == (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y))]
with selected values for X and Y:

    (Math::Tanh(0.1) + Math::Tanh(1.2)) /
(1 + Math::Tanh(0.1) * Math::Tanh(1.2)) == 8.6172315931330645E-001
                        Math::Tanh(1.3) == 8.6172315931330634E-001

    (Math::Tanh(1.2) + Math::Tanh(4.9)) /
(1 + Math::Tanh(1.2) * Math::Tanh(4.9)) == 9.9998993913939649E-001
                        Math::Tanh(6.1) == 9.9998993913939649E-001
*/