Handling Higher Math





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Handling Higher Math

Well, it may have been a mistake taking on that programming job from the astrophysics department. How do you calculate a hyperbolic cosecant anyway? Can Visual Basic do it? Yes, although not directly. The built-in Visual Basic math functions appear in Table 2.8-note that the old VB6 functions like Atn and Abs have been replaced by methods of the System.Math namespace.

Table 2.8: Math methods.

Old

New Visual Basic .NET method

Description

Abs

System.Math.Abs

Yields the absolute value of a given number.

Atn

System.Math.Atan

Yields a Double value containing the angle whose tangent is the given number.

Cos

System.Math.Cos

Yields a Double value containing the cosine of the given angle.

Exp

System.Math.Exp

Yields a Double value containing e (the base of natural logarithms) raised to the given power.

Log

System.Math.Log

Yields a Double value containing the logarithm of a given number.

Round

System.Math.Round

Yields a Double value containing the number nearest the given value.

Sgn

System.Math.Sign

Yields an Integer value indicating the sign of a number.

Sin

System.Math.Sin

Yields a Double value specifying the sine of an angle.

Sqr

System.Math.Sqrt

Yields a Double value specifying the square root of a number.

Tan

System.Math.Tan

Yields a Double value containing the tangent of an angle.

To use these functions without qualification, import the System.Math namespace into your project. Here's an example that uses the Atan method:

Imports System.Math
Module Module1
    Sub Main()
        System.Console.WriteLine("Pi =" & 4 * Atan(1))
    End Sub
End Module

And here's the result:

Pi =3.14159265358979
Press any key to continue

If what you want, like hyperbolic cosecant, is not in Table 2.8, try Table 2.9, which shows you how to calculate other results using the built-in Visual Basic functions. There's enough math power in Table 2.9 to keep most astrophysicists happy.

Table 2.9: Calculated math functions.

Function

Calculate this way

Secant

Sec(X) = 1 / Cos(X)

Cosecant

Cosec(X) = 1 / Sin(X)

Cotangent

Cotan(X) = 1 / Tan(X)

Inverse Sine

Arcsin(X) = Atn(X / Sqr(-X * X + 1))

Inverse Cosine

Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)

Inverse Secant

Arcsec(X) = Atn(X / Sqr(X * X - 1)) + Sgn((X) - 1) * (2 * Atn(1))

Inverse Cosecant

Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))

Inverse Cotangent

Arccotan(X) = Atn(X) + 2 * Atn(1)

Hyperbolic Sine

HSin(X) = (Exp(X) - Exp(-X)) / 2

Hyperbolic Cosine

HCos(X) = (Exp(X) + Exp(-X)) / 2

Hyperbolic Tangent

HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))

Hyperbolic Secant

HSec(X) = 2 / (Exp(X) + Exp(-X))

Hyperbolic Cosecant

HCosec(X) = 2 / (Exp(X) - Exp(-X))

Hyperbolic Cotangent

HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))

Inverse Hyperbolic Sine

HArcsin(X) = Log(X + Sqr(X * X + 1))

Inverse Hyperbolic Cosine

HArccos(X) = Log(X + Sqr(X * X - 1))

Inverse Hyperbolic Tangent

HArctan(X) = Log((1 + X) / (1 - X)) / 2

Inverse Hyperbolic Secant

HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)

Inverse Hyperbolic Cosecant

HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)

Inverse Hyperbolic Cotangent

HArccotan(X) = Log((X + 1) / (X - 1)) / 2

Logarithm to base N

LogN(X) = Log(X) / Log(N)

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