Math.Cosh(Double) メソッド

定義

指定された角度のハイパーボリック コサインを返します。Returns the hyperbolic cosine of the specified angle.

public:
 static double Cosh(double value);
public static double Cosh (double value);
static member Cosh : double -> double
Public Shared Function Cosh (value As Double) As Double

パラメーター

value
Double

ラジアンで表した角度。An angle, measured in radians.

戻り値

Double

value のハイパーボリック コサイン。The hyperbolic cosine of value. valueNegativeInfinity または PositiveInfinity に等しい場合は、PositiveInfinity が返されます。If value is equal to NegativeInfinity or PositiveInfinity, PositiveInfinity is returned. valueNaN に等しい場合は、NaN が返されます。If value is equal to NaN, NaN is returned.

次の例では、を使用し Cosh て、選択した値の特定のハイパーボリック id を評価します。The following example uses Cosh to evaluate certain hyperbolic identities for selected values.

// Example for the hyperbolic Math.Sinh( double ) 
// and Math.Cosh( double ) methods.
using namespace System;

// Evaluate hyperbolic identities with a given argument.
void UseSinhCosh( double arg )
{
   double sinhArg = Math::Sinh( arg );
   double coshArg = Math::Cosh( arg );
   
   // Evaluate cosh^2(X) - sinh^2(X) == 1.
   Console::WriteLine( "\n                          Math::Sinh({0}) == {1:E16}\n"
   "                          Math::Cosh({0}) == {2:E16}", arg, Math::Sinh( arg ), Math::Cosh( arg ) );
   Console::WriteLine( "(Math::Cosh({0}))^2 - (Math::Sinh({0}))^2 == {1:E16}", arg, coshArg * coshArg - sinhArg * sinhArg );
   
   // Evaluate sinh(2 * X) == 2 * sinh(X) * cosh(X).
   Console::WriteLine( "                          Math::Sinh({0}) == {1:E16}", 2.0 * arg, Math::Sinh( 2.0 * arg ) );
   Console::WriteLine( "    2 * Math::Sinh({0}) * Math::Cosh({0}) == {1:E16}", arg, 2.0 * sinhArg * coshArg );
   
   // Evaluate cosh(2 * X) == cosh^2(X) + sinh^2(X).
   Console::WriteLine( "                          Math::Cosh({0}) == {1:E16}", 2.0 * arg, Math::Cosh( 2.0 * arg ) );
   Console::WriteLine( "(Math::Cosh({0}))^2 + (Math::Sinh({0}))^2 == {1:E16}", arg, coshArg * coshArg + sinhArg * sinhArg );
}


// Evaluate hyperbolic identities that are functions of two arguments.
void UseTwoArgs( double argX, double argY )
{
   
   // Evaluate sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
   Console::WriteLine( "\n        Math::Sinh({0}) * Math::Cosh({1}) +\n"
   "        Math::Cosh({0}) * Math::Sinh({1}) == {2:E16}", argX, argY, Math::Sinh( argX ) * Math::Cosh( argY ) + Math::Cosh( argX ) * Math::Sinh( argY ) );
   Console::WriteLine( "                          Math::Sinh({0}) == {1:E16}", argX + argY, Math::Sinh( argX + argY ) );
   
   // Evaluate cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
   Console::WriteLine( "        Math::Cosh({0}) * Math::Cosh({1}) +\n"
   "        Math::Sinh({0}) * Math::Sinh({1}) == {2:E16}", argX, argY, Math::Cosh( argX ) * Math::Cosh( argY ) + Math::Sinh( argX ) * Math::Sinh( argY ) );
   Console::WriteLine( "                          Math::Cosh({0}) == {1:E16}", argX + argY, Math::Cosh( argX + argY ) );
}

int main()
{
   Console::WriteLine( "This example of hyperbolic "
   "Math::Sinh( double ) and Math::Cosh( double )\n"
   "generates the following output.\n" );
   Console::WriteLine( "Evaluate these hyperbolic identities "
   "with selected values for X:" );
   Console::WriteLine( "   cosh^2(X) - sinh^2(X) == 1\n"
   "   sinh(2 * X) == 2 * sinh(X) * cosh(X)" );
   Console::WriteLine( "   cosh(2 * X) == cosh^2(X) + sinh^2(X)" );
   UseSinhCosh( 0.1 );
   UseSinhCosh( 1.2 );
   UseSinhCosh( 4.9 );
   Console::WriteLine( "\nEvaluate these hyperbolic identities "
   "with selected values for X and Y:" );
   Console::WriteLine( "   sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y)" );
   Console::WriteLine( "   cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y)" );
   UseTwoArgs( 0.1, 1.2 );
   UseTwoArgs( 1.2, 4.9 );
}

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

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

                          Math::Sinh(0.1) == 1.0016675001984403E-001
                          Math::Cosh(0.1) == 1.0050041680558035E+000
(Math::Cosh(0.1))^2 - (Math::Sinh(0.1))^2 == 9.9999999999999989E-001
                          Math::Sinh(0.2) == 2.0133600254109399E-001
    2 * Math::Sinh(0.1) * Math::Cosh(0.1) == 2.0133600254109396E-001
                          Math::Cosh(0.2) == 1.0200667556190759E+000
(Math::Cosh(0.1))^2 + (Math::Sinh(0.1))^2 == 1.0200667556190757E+000

                          Math::Sinh(1.2) == 1.5094613554121725E+000
                          Math::Cosh(1.2) == 1.8106555673243747E+000
(Math::Cosh(1.2))^2 - (Math::Sinh(1.2))^2 == 1.0000000000000000E+000
                          Math::Sinh(2.4) == 5.4662292136760939E+000
    2 * Math::Sinh(1.2) * Math::Cosh(1.2) == 5.4662292136760939E+000
                          Math::Cosh(2.4) == 5.5569471669655064E+000
(Math::Cosh(1.2))^2 + (Math::Sinh(1.2))^2 == 5.5569471669655064E+000

                          Math::Sinh(4.9) == 6.7141166550932297E+001
                          Math::Cosh(4.9) == 6.7148613134003227E+001
(Math::Cosh(4.9))^2 - (Math::Sinh(4.9))^2 == 1.0000000000000000E+000
                          Math::Sinh(9.8) == 9.0168724361884615E+003
    2 * Math::Sinh(4.9) * Math::Cosh(4.9) == 9.0168724361884615E+003
                          Math::Cosh(9.8) == 9.0168724916400624E+003
(Math::Cosh(4.9))^2 + (Math::Sinh(4.9))^2 == 9.0168724916400606E+003

Evaluate these hyperbolic identities with selected values for X and Y:
   sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y)
   cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y)

        Math::Sinh(0.1) * Math::Cosh(1.2) +
        Math::Cosh(0.1) * Math::Sinh(1.2) == 1.6983824372926155E+000
                          Math::Sinh(1.3) == 1.6983824372926160E+000
        Math::Cosh(0.1) * Math::Cosh(1.2) +
        Math::Sinh(0.1) * Math::Sinh(1.2) == 1.9709142303266281E+000
                          Math::Cosh(1.3) == 1.9709142303266285E+000

        Math::Sinh(1.2) * Math::Cosh(4.9) +
        Math::Cosh(1.2) * Math::Sinh(4.9) == 2.2292776360739879E+002
                          Math::Sinh(6.1) == 2.2292776360739885E+002
        Math::Cosh(1.2) * Math::Cosh(4.9) +
        Math::Sinh(1.2) * Math::Sinh(4.9) == 2.2293000647511826E+002
                          Math::Cosh(6.1) == 2.2293000647511832E+002
*/
// Example for the hyperbolic Math.Sinh( double )
// and Math.Cosh( double ) methods.
using System;

class SinhCosh
{
    public static void Main()
    {
        Console.WriteLine(
            "This example of hyperbolic Math.Sinh( double ) " +
            "and Math.Cosh( double )\n" +
            "generates the following output.\n" );
        Console.WriteLine(
            "Evaluate these hyperbolic identities " +
            "with selected values for X:" );
        Console.WriteLine(
            "   cosh^2(X) - sinh^2(X) == 1\n" +
            "   sinh(2 * X) == 2 * sinh(X) * cosh(X)" );
        Console.WriteLine( "   cosh(2 * X) == cosh^2(X) + sinh^2(X)" );

        UseSinhCosh(0.1);
        UseSinhCosh(1.2);
        UseSinhCosh(4.9);

        Console.WriteLine(
            "\nEvaluate these hyperbolic identities " +
            "with selected values for X and Y:" );
        Console.WriteLine(
            "   sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y)" );
        Console.WriteLine(
            "   cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y)" );

        UseTwoArgs(0.1, 1.2);
        UseTwoArgs(1.2, 4.9);
    }

    // Evaluate hyperbolic identities with a given argument.
    static void UseSinhCosh(double arg)
    {
        double sinhArg = Math.Sinh(arg);
        double coshArg = Math.Cosh(arg);

        // Evaluate cosh^2(X) - sinh^2(X) == 1.
        Console.WriteLine(
            "\n                         Math.Sinh({0}) == {1:E16}\n" +
            "                         Math.Cosh({0}) == {2:E16}",
            arg, Math.Sinh(arg), Math.Cosh(arg) );
        Console.WriteLine(
            "(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 == {1:E16}",
            arg, coshArg * coshArg - sinhArg * sinhArg );

        // Evaluate sinh(2 * X) == 2 * sinh(X) * cosh(X).
        Console.WriteLine(
            "                         Math.Sinh({0}) == {1:E16}",
            2.0 * arg, Math.Sinh(2.0 * arg) );
        Console.WriteLine(
            "    2 * Math.Sinh({0}) * Math.Cosh({0}) == {1:E16}",
            arg, 2.0 * sinhArg * coshArg );

        // Evaluate cosh(2 * X) == cosh^2(X) + sinh^2(X).
        Console.WriteLine(
            "                         Math.Cosh({0}) == {1:E16}",
            2.0 * arg, Math.Cosh(2.0 * arg) );
        Console.WriteLine(
            "(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 == {1:E16}",
            arg, coshArg * coshArg + sinhArg * sinhArg );
    }

    // Evaluate hyperbolic identities that are functions of two arguments.
    static void UseTwoArgs(double argX, double argY)
    {
        // Evaluate sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
        Console.WriteLine(
            "\n        Math.Sinh({0}) * Math.Cosh({1}) +\n" +
            "        Math.Cosh({0}) * Math.Sinh({1}) == {2:E16}",
            argX, argY, Math.Sinh(argX) * Math.Cosh(argY) +
            Math.Cosh(argX) * Math.Sinh(argY));
        Console.WriteLine(
            "                         Math.Sinh({0}) == {1:E16}",
            argX + argY, Math.Sinh(argX + argY));

        // Evaluate cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
        Console.WriteLine(
            "        Math.Cosh({0}) * Math.Cosh({1}) +\n" +
            "        Math.Sinh({0}) * Math.Sinh({1}) == {2:E16}",
            argX, argY, Math.Cosh(argX) * Math.Cosh(argY) +
            Math.Sinh(argX) * Math.Sinh(argY));
        Console.WriteLine(
            "                         Math.Cosh({0}) == {1:E16}",
            argX + argY, Math.Cosh(argX + argY));
    }
}

/*
This example of hyperbolic Math.Sinh( double ) and Math.Cosh( double )
generates the following output.

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

                         Math.Sinh(0.1) == 1.0016675001984403E-001
                         Math.Cosh(0.1) == 1.0050041680558035E+000
(Math.Cosh(0.1))^2 - (Math.Sinh(0.1))^2 == 9.9999999999999989E-001
                         Math.Sinh(0.2) == 2.0133600254109399E-001
    2 * Math.Sinh(0.1) * Math.Cosh(0.1) == 2.0133600254109396E-001
                         Math.Cosh(0.2) == 1.0200667556190759E+000
(Math.Cosh(0.1))^2 + (Math.Sinh(0.1))^2 == 1.0200667556190757E+000

                         Math.Sinh(1.2) == 1.5094613554121725E+000
                         Math.Cosh(1.2) == 1.8106555673243747E+000
(Math.Cosh(1.2))^2 - (Math.Sinh(1.2))^2 == 1.0000000000000000E+000
                         Math.Sinh(2.4) == 5.4662292136760939E+000
    2 * Math.Sinh(1.2) * Math.Cosh(1.2) == 5.4662292136760939E+000
                         Math.Cosh(2.4) == 5.5569471669655064E+000
(Math.Cosh(1.2))^2 + (Math.Sinh(1.2))^2 == 5.5569471669655064E+000

                         Math.Sinh(4.9) == 6.7141166550932297E+001
                         Math.Cosh(4.9) == 6.7148613134003227E+001
(Math.Cosh(4.9))^2 - (Math.Sinh(4.9))^2 == 1.0000000000000000E+000
                         Math.Sinh(9.8) == 9.0168724361884615E+003
    2 * Math.Sinh(4.9) * Math.Cosh(4.9) == 9.0168724361884615E+003
                         Math.Cosh(9.8) == 9.0168724916400624E+003
(Math.Cosh(4.9))^2 + (Math.Sinh(4.9))^2 == 9.0168724916400606E+003

Evaluate these hyperbolic identities with selected values for X and Y:
   sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y)
   cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y)

        Math.Sinh(0.1) * Math.Cosh(1.2) +
        Math.Cosh(0.1) * Math.Sinh(1.2) == 1.6983824372926155E+000
                         Math.Sinh(1.3) == 1.6983824372926160E+000
        Math.Cosh(0.1) * Math.Cosh(1.2) +
        Math.Sinh(0.1) * Math.Sinh(1.2) == 1.9709142303266281E+000
                         Math.Cosh(1.3) == 1.9709142303266285E+000

        Math.Sinh(1.2) * Math.Cosh(4.9) +
        Math.Cosh(1.2) * Math.Sinh(4.9) == 2.2292776360739879E+002
                         Math.Sinh(6.1) == 2.2292776360739885E+002
        Math.Cosh(1.2) * Math.Cosh(4.9) +
        Math.Sinh(1.2) * Math.Sinh(4.9) == 2.2293000647511826E+002
                         Math.Cosh(6.1) == 2.2293000647511832E+002
*/
' Example for the hyperbolic Math.Sinh( Double ) and Math.Cosh( Double ) methods.
Module SinhCosh
   
    Sub Main()
        Console.WriteLine( _
            "This example of hyperbolic " & _
            "Math.Sinh( Double ) and Math.Cosh( Double )" & vbCrLf & _
            "generates the following output." & vbCrLf)
        Console.WriteLine( _
            "Evaluate these hyperbolic identities " & _
            "with selected values for X:")
        Console.WriteLine( _
            "   cosh^2(X) - sinh^2(X) = 1" & vbCrLf & _
            "   sinh(2 * X) = 2 * sinh(X) * cosh(X)")
        Console.WriteLine("   cosh(2 * X) = cosh^2(X) + sinh^2(X)")
          
        UseSinhCosh(0.1)
        UseSinhCosh(1.2)
        UseSinhCosh(4.9)
          
        Console.WriteLine( _
            vbCrLf & "Evaluate these hyperbolic " & _
            "identities with selected values for X and Y:")
        Console.WriteLine( _
            "   sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y)")
        Console.WriteLine( _
            "   cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y)")

        UseTwoArgs(0.1, 1.2)
        UseTwoArgs(1.2, 4.9)
    End Sub
      
    ' Evaluate hyperbolic identities with a given argument.
    Sub UseSinhCosh(arg As Double)
        Dim sinhArg As Double = Math.Sinh(arg)
        Dim coshArg As Double = Math.Cosh(arg)
          
        ' Evaluate cosh^2(X) - sinh^2(X) = 1.
        Console.WriteLine( _
            vbCrLf & "                         Math.Sinh({0}) = {1:E16}" + _
            vbCrLf & "                         Math.Cosh({0}) = {2:E16}", _
            arg, Math.Sinh(arg), Math.Cosh(arg))
        Console.WriteLine( _
            "(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 = {1:E16}", _
            arg, coshArg * coshArg - sinhArg * sinhArg)
          
        ' Evaluate sinh(2 * X) = 2 * sinh(X) * cosh(X).
        Console.WriteLine( _
            "                         Math.Sinh({0}) = {1:E16}", _
            2.0 * arg, Math.Sinh((2.0 * arg)))
        Console.WriteLine( _
            "    2 * Math.Sinh({0}) * Math.Cosh({0}) = {1:E16}", _
            arg, 2.0 * sinhArg * coshArg)
          
        ' Evaluate cosh(2 * X) = cosh^2(X) + sinh^2(X).
        Console.WriteLine( _
            "                         Math.Cosh({0}) = {1:E16}", _
            2.0 * arg, Math.Cosh((2.0 * arg)))
        Console.WriteLine( _
            "(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 = {1:E16}", _
            arg, coshArg * coshArg + sinhArg * sinhArg)

    End Sub
       
    ' Evaluate hyperbolic identities that are functions of two arguments.
    Sub UseTwoArgs(argX As Double, argY As Double)

        ' Evaluate sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
        Console.WriteLine( _
            vbCrLf & "        Math.Sinh({0}) * Math.Cosh({1}) +" + _
            vbCrLf & "        Math.Cosh({0}) * Math.Sinh({1}) = {2:E16}", _
            argX, argY, Math.Sinh(argX) * Math.Cosh(argY) + _
            Math.Cosh(argX) * Math.Sinh(argY))
        Console.WriteLine( _
            "                         Math.Sinh({0}) = {1:E16}", _
            argX + argY, Math.Sinh((argX + argY)))
          
        ' Evaluate cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
        Console.WriteLine( _
            "        Math.Cosh({0}) * Math.Cosh({1}) +" + _
            vbCrLf & "        Math.Sinh({0}) * Math.Sinh({1}) = {2:E16}", _
            argX, argY, Math.Cosh(argX) * Math.Cosh(argY) + _
            Math.Sinh(argX) * Math.Sinh(argY))
        Console.WriteLine( _
            "                         Math.Cosh({0}) = {1:E16}", _
            argX + argY, Math.Cosh((argX + argY)))

    End Sub
End Module 'SinhCosh

' This example of hyperbolic Math.Sinh( Double ) and Math.Cosh( Double )
' generates the following output.
' 
' Evaluate these hyperbolic identities with selected values for X:
'    cosh^2(X) - sinh^2(X) = 1
'    sinh(2 * X) = 2 * sinh(X) * cosh(X)
'    cosh(2 * X) = cosh^2(X) + sinh^2(X)
' 
'                          Math.Sinh(0.1) = 1.0016675001984403E-001
'                          Math.Cosh(0.1) = 1.0050041680558035E+000
' (Math.Cosh(0.1))^2 - (Math.Sinh(0.1))^2 = 9.9999999999999989E-001
'                          Math.Sinh(0.2) = 2.0133600254109399E-001
'     2 * Math.Sinh(0.1) * Math.Cosh(0.1) = 2.0133600254109396E-001
'                          Math.Cosh(0.2) = 1.0200667556190759E+000
' (Math.Cosh(0.1))^2 + (Math.Sinh(0.1))^2 = 1.0200667556190757E+000
' 
'                          Math.Sinh(1.2) = 1.5094613554121725E+000
'                          Math.Cosh(1.2) = 1.8106555673243747E+000
' (Math.Cosh(1.2))^2 - (Math.Sinh(1.2))^2 = 1.0000000000000000E+000
'                          Math.Sinh(2.4) = 5.4662292136760939E+000
'     2 * Math.Sinh(1.2) * Math.Cosh(1.2) = 5.4662292136760939E+000
'                          Math.Cosh(2.4) = 5.5569471669655064E+000
' (Math.Cosh(1.2))^2 + (Math.Sinh(1.2))^2 = 5.5569471669655064E+000
' 
'                          Math.Sinh(4.9) = 6.7141166550932297E+001
'                          Math.Cosh(4.9) = 6.7148613134003227E+001
' (Math.Cosh(4.9))^2 - (Math.Sinh(4.9))^2 = 1.0000000000000000E+000
'                          Math.Sinh(9.8) = 9.0168724361884615E+003
'     2 * Math.Sinh(4.9) * Math.Cosh(4.9) = 9.0168724361884615E+003
'                          Math.Cosh(9.8) = 9.0168724916400624E+003
' (Math.Cosh(4.9))^2 + (Math.Sinh(4.9))^2 = 9.0168724916400606E+003
' 
' Evaluate these hyperbolic identities with selected values for X and Y:
'    sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y)
'    cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y)
' 
'         Math.Sinh(0.1) * Math.Cosh(1.2) +
'         Math.Cosh(0.1) * Math.Sinh(1.2) = 1.6983824372926155E+000
'                          Math.Sinh(1.3) = 1.6983824372926160E+000
'         Math.Cosh(0.1) * Math.Cosh(1.2) +
'         Math.Sinh(0.1) * Math.Sinh(1.2) = 1.9709142303266281E+000
'                          Math.Cosh(1.3) = 1.9709142303266285E+000
' 
'         Math.Sinh(1.2) * Math.Cosh(4.9) +
'         Math.Cosh(1.2) * Math.Sinh(4.9) = 2.2292776360739879E+002
'                          Math.Sinh(6.1) = 2.2292776360739885E+002
'         Math.Cosh(1.2) * Math.Cosh(4.9) +
'         Math.Sinh(1.2) * Math.Sinh(4.9) = 2.2293000647511826E+002
'                          Math.Cosh(6.1) = 2.2293000647511832E+002

注釈

角度は、 value ラジアンで指定する必要があります。The angle, value, must be in radians. 角度を Math.PI ラジアンに変換するには、/180 を乗算します。Multiply by Math.PI/180 to convert degrees to radians.

このメソッドは、基になる C ランタイムを呼び出します。正確な結果または有効な入力範囲は、オペレーティングシステムまたはアーキテクチャによって異なる場合があります。This method calls into the underlying C runtime, and the exact result or valid input range may differ between different operating systems or architectures.

適用対象