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# Elementary Transcendental Functions

 Exp[z] exponential function ez Log[z] logarithm loge (z) Log[b,z] logarithm logb (z) to base b Log2[z], Log10[z] logarithm to base 2 and 10 Sin[z], Cos[z], Tan[z], Csc[z], Sec[z], Cot[z] trigonometric functions (with arguments in radians) ArcSin[z], ArcCos[z], ArcTan[z], ArcCsc[z], ArcSec[z], ArcCot[z] inverse trigonometric functions (giving results in radians) ArcTan[x,y] the argument of x+iy Sinh[z], Cosh[z], Tanh[z], Csch[z], Sech[z], Coth[z] hyperbolic functions ArcSinh[z], ArcCosh[z], ArcTanh[z], ArcCsch[z], ArcSech[z], ArcCoth[z] inverse hyperbolic functions Sinc[z] sinc function sin (z)/z Haversine[z] haversine function hav (z) InverseHaversine[z] inverse haversine function hav-1 (z) Gudermannian[z] Gudermannian function gd (z) InverseGudermannian[z] inverse Gudermannian function gd-1 (z)

Elementary transcendental functions.

Mathematica gives exact results for logarithms whenever it can. Here is log21024.
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You can find the numerical values of mathematical functions to any precision.
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This gives a complex number result.
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Mathematica can evaluate logarithms with complex arguments.
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The arguments of trigonometric functions are always given in radians.
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You can convert from degrees by explicitly multiplying by the constant Degree.
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Here is a plot of the hyperbolic tangent function. It has a characteristic "sigmoidal" form.
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The haversine function Haversine[z] is defined by sin2 (z/2). The inverse haversine function is defined by . The Gudermannian function Gudermannian[z] is defined as . The inverse Gudermannian function is defined by gd-1 (z)=log[tan (z/2+/4)]. The Gudermannian satisfies such relations as sinh (z)=tan[gd (x)]. The sinc function 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 eix is sometimes written as cis (x).