Mathematica Tutorial

Elementary Transcendental Functions

Exp[z]	exponential function e^z
Log[z]	logarithm log_e (z)
Log[b,z]	logarithm log_b (z) to base b
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

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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There are a number of additional trigonometric and hyperbolic functions that are sometimes used. The versine function is defined as vers (z)=1-cos (z). The haversine is simply

. The complex exponential e^ix is sometimes written as cis (x). The Gudermannian function is defined as

. The inverse Gudermannian is gd^-1 (z)=log[sec (z)+tan (z)]. The Gudermannian satisfies such relations as sinh (z)=tan[gd (x)]. The sinc function Sinc[z] is the Fourier transform of a square signal.