ArcCot

ArcCot[z]
gives the arc cotangent of the complex number
.
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- All results are given in radians.
- For real
, the results are always in the range
to
, excluding 0.
- For certain special arguments, ArcCot automatically evaluates to exact values.
- ArcCot can be evaluated to arbitrary numerical precision.
- ArcCot automatically threads over lists.
- ArcCot[z] has a branch cut discontinuity in the complex
plane running from
to
.
- ArcCot can be used with Interval and CenteredInterval objects. »
Background & Context
- ArcCot is the inverse cotangent function. For a real number
, ArcCot[x] represents the radian angle measure
(excluding 0) such that
.
- ArcCot automatically threads over lists. For certain special arguments, ArcCot automatically evaluates to exact values. When given exact numeric expressions as arguments, ArcCot may be evaluated to arbitrary numeric precision. Operations useful for manipulation of symbolic expressions involving ArcCot include FunctionExpand, TrigToExp, TrigExpand, Simplify, and FullSimplify.
- ArcCot is defined for complex argument
via
. ArcCot[z] has a branch cut discontinuity in the complex
plane.
- Related mathematical functions include Cot, ArcTan, and ArcCoth.
Examples
open allclose allBasic Examples (5)
Scope (46)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate ArcCot efficiently at high precision:
ArcCot threads elementwise over lists and matrices:
ArcCot can be used with Interval and CenteredInterval objects:
Specific Values (4)
Visualization (3)
Function Properties (12)
ArcCot is defined for all real values:
ArcCot achieves all real values except 0 from the interval :
Function range for arguments from the complex domain:
ArcCot is an odd function:
ArcCot has the mirror property :
ArcCot is not an analytic function:
ArcCot is neither non-decreasing nor non-increasing:
ArcCot is injective:
ArcCot is not surjective:
ArcCot is neither non-negative nor non-positive:
ArcCot has both singularity and discontinuity at zero:
ArcCot is neither convex nor concave:
TraditionalForm formatting:
Integration (3)
Series Expansions (4)
Integral Transforms (3)
Compute the inverse Laplace transform using InverseLaplaceTransform:
Function Identities and Simplifications (3)
Function Representations (5)
Represent using ArcTan:
Representation through inverse Jacobi functions:
Represent using Hypergeometric2F1:
Representation in terms of MeijerG:
ArcCot can be represented as a DifferentialRoot:
Applications (4)
Find angles of the right triangle with sides 3, 4 and hypotenuse 5:
Addition theorem for cotangent function:
Solve a differential equation:
Branch cut of ArcCot runs along the imaginary axis:
RelatedLinks-Functions.png
RelatedLinks-Functions.png
RelatedLinks-Functions.png
RelatedLinks-Functions.png
RelatedLinks-Functions.png
RelatedLinks-Functions.png
RelatedLinks-Functions.png
RelatedLinks-Functions.png
RelatedLinks-Functions.png
RelatedLinks-Functions.png