ArcCos

ArcCos[z]

gives the arc cosine of the complex number .

Details

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

Background & Context

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

Examples

open allclose all

Basic Examples  (3)

Results are in radians:

In[1]:=
Click for copyable input
Out[1]=

Plot over a subset of the reals:

In[1]:=
Click for copyable input
Out[1]=

Series expansion:

In[1]:=
Click for copyable input
Out[1]=

Scope  (6)

Generalizations & Extensions  (6)

Applications  (3)

Properties & Relations  (10)

Possible Issues  (3)

Neat Examples  (2)

See Also

Cos  ArcSin  ArcCosh  Degree  VectorAngle  TrigToExp  TrigExpand

Tutorials

Introduced in 1988
(1.0)