Elementary Transcendental Functions

Elementary transcendental functions.

The Wolfram Language gives exact results for logarithms whenever it can. Here is (Subscript[log, 2])1024:

Log[2,1024]

You can find the numerical values of mathematical functions to any precision:

N[Log[2],40]

This gives a complex number result:

N[Log[-2]]

The Wolfram Language can evaluate logarithms with complex arguments:

N[Log[2+8 I]]

The arguments of trigonometric functions are always given in radians:

Sin[Pi/2]

You can convert from degrees by explicitly multiplying by the constant (RefLink[Degree, paclet:ref/Degree]):

N[Sin[30 Degree]]

Here is a plot of the hyperbolic tangent function. It has a characteristic "sigmoidal" form:

Plot[Tanh[x],{x,-8,8}]

The haversine function (RefLink[Haversine, paclet:ref/Haversine])[z] is defined by (sin^2)(z/2). The inverse haversine function (RefLink[InverseHaversine, paclet:ref/InverseHaversine])[z] is defined by 2 (sin^(-1))((Sqrt[z])). The Gudermannian function (RefLink[Gudermannian, paclet:ref/Gudermannian])[z] is defined as gd(z)==2(tan^(-1))((e^z))-(π/2). The inverse Gudermannian function (RefLink[InverseGudermannian, paclet:ref/InverseGudermannian])[z] is defined by (gd^(-1))(z)==log[tan(z/2+π/4)]. The Gudermannian satisfies such relations as sinh(z)==tan[gd(x)]. The sinc function (RefLink[Sinc, paclet:ref/Sinc])[z] is the Fourier transform of a square signal.

There are a number of additional trigonometric and hyperbolic functions that are sometimes used. The versine function is sometimes encountered in the literature and simply is vers(z)==2hav(z). The coversine function is defined as covers(z)==1-sin(z). The complex exponential (e^(ix)) is sometimes written as cis(x).