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 The built-in Visual Basic math functions appear in Table 2.8-note that the old VB6 functions like Atn and Abs have been replaced by methods of the System.Math namespace.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)