# ArcCsc

ArcCsc[z]

gives the arc cosecant of the complex number .

# Details

• Mathematical function, suitable for both symbolic and numerical manipulation.
• All results are given in radians.
• For real z outside the interval to , the results are always in the range to , excluding 0.
• For certain special arguments, ArcCsc automatically evaluates to exact values.
• ArcCsc can be evaluated to arbitrary numerical precision.
• ArcCsc automatically threads over lists.
• ArcCsc[z] has a branch cut discontinuity in the complex plane running from to .

# Background & Context

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

# 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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