# ArcCosh

ArcCosh[z]

gives the inverse hyperbolic cosine of the complex number .

# Details

• Mathematical function, suitable for both symbolic and numerical manipulation.
• For certain special arguments, ArcCosh automatically evaluates to exact values.
• ArcCosh can be evaluated to arbitrary numerical precision.
• ArcCosh automatically threads over lists.
• ArcCosh[z] has a branch cut discontinuity in the complex plane running from to .

# Background & Context

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

# Examples

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## Basic Examples(3)

Evaluate numerically:

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Plot over a subset of the reals:

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Series expansion:

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