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 .
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)
Specific Values (4)
Plot the ArcCot function:
Function Properties (5)
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.
Wolfram Language. 1988. "ArcCot." Wolfram Language & System Documentation Center. Wolfram Research. 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