BUILT-IN MATHEMATICA SYMBOL

ArcSec

ArcSec[z]
gives the arc secant

of the complex number

.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

All results are given in radians.

For real outside the interval to , the results are always in the range to , excluding .

For certain special arguments, ArcSec automatically evaluates to exact values.

ArcSec can be evaluated to arbitrary numerical precision.

ArcSec automatically threads over lists.

ArcSec[z] has a branch cut discontinuity in the complex plane running from to .

EXAMPLES

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Basic Examples (3)

Result in radians:

Series expansion:

Result in radians:

In[1]:=

Out[1]=

In[1]:=

Out[1]=

Series expansion:

In[1]:=

Out[1]=

Scope (6)

Evaluate numerically:

Evaluate for complex arguments:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Simple exact values are generated automatically:

TraditionalForm formatting:

Generalizations & Extensions (5)

ArcSec can deal with real-valued intervals:

Infinite arguments give symbolic results:

ArcSec can be applied to power series:

Find series expansions at branch points and branch cuts:

ArcSec threads over explicit lists as well as over sparse arrays:

Applications (1)

Branch cut of ArcSec runs along the real axis:

Properties & Relations (5)

Compose with inverse functions:

Use PowerExpand to disregard multivaluedness of the ArcSec:

Alternatively, evaluate under additional assumptions:

Use TrigToExp to express in terms of logarithm:

Use ExpToTrig to convert back:

Integrals:

Use FunctionExpand to convert trigs of arctrigs into an algebraic function:

Simplify result:

Use Reduce to solve equations involving ArcSec: