gives the arc cotangent of the complex number .
- 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.
Examplesopen allclose all
Basic Examples (5)
Numerical Evaluation (6)
Evaluate ArcCot efficiently at high precision:
ArcCot threads elementwise over lists and matrices:
Specific Values (4)
Plot the ArcCot function:
Function Properties (12)
ArcCot is defined for all real values:
ArcCot achieves all real values except 0 from the interval :
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:
Series Expansions (4)
Integral Transforms (3)
Function Identities and Simplifications (3)
Branch cut of ArcCot runs along the imaginary axis:
Wolfram Research (1988), ArcCot, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCot.html (updated 2021).
Wolfram Language. 1988. "ArcCot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/ArcCot.html.
Wolfram Language. (1988). ArcCot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCot.html