# ArcSec

ArcSec[z]

gives the arc secant of the complex number .

# Details

• 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 .

# Background & Context

• ArcSec is the inverse secant function. For a real number , ArcSec[x] represents the radian angle measure, , , such that .
• ArcSec automatically threads over lists. For certain special arguments, ArcSec automatically evaluates to exact values. When given exact numeric expressions as arguments, ArcSec may be evaluated to arbitrary numeric precision. Operations useful for manipulation of symbolic expressions involving ArcSec include FunctionExpand, TrigToExp, TrigExpand, Simplify, and FullSimplify.
• ArcSec is defined for complex argument via . ArcSec[z] has a branch cut discontinuity in the complex plane.
• Related mathematical functions include Sec, ArcCsc, and ArcSech.

# Examples

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## Basic Examples(3)

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Plot over a subset of the reals:

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Series expansion:

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