gives the arc cosecant of the complex number .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- All results are given in radians.
- For real z outside the interval to , the results are always in the range to , excluding 0.
- For certain special arguments, ArcCsc automatically evaluates to exact values.
- ArcCsc can be evaluated to arbitrary numerical precision.
- ArcCsc automatically threads over lists.
- ArcCsc[z] has a branch cut discontinuity in the complex plane running from to .
- ArcCsc can be used with Interval and CenteredInterval objects. »
Background & Context
- ArcCsc is the inverse cosecant function. For a real number , ArcCsc[x] represents the radian angle measure , , such that .
- ArcCsc automatically threads over lists. For certain special arguments, ArcCsc automatically evaluates to exact values. When given exact numeric expressions as arguments, ArcCsc may be evaluated to arbitrary numeric precision. Operations useful for manipulation of symbolic expressions involving ArcCsc include FunctionExpand, TrigToExp, TrigExpand, Simplify, and FullSimplify.
- ArcCsc is defined for complex argument via . ArcCsc[z] has a branch cut discontinuity in the complex plane.
- Related mathematical functions include Csc, ArcSec, and ArcCsch.
Examplesopen allclose all
Basic Examples (5)
Numerical Evaluation (6)
Evaluate ArcCsc efficiently at high precision:
ArcCsc threads elementwise over lists and matrices:
Specific Values (4)
ArcCsc is not differentiable at these points:
Plot the ArcCsc function:
Function Properties (11)
ArcCsc is defined for all real values except from the interval :
ArcCsc achieves all real values from the interval except 0:
ArcCsc is an odd function:
ArcCsc is not an analytic function:
ArcCsc is monotonic in a specific range:
ArcCsc is injective:
ArcCsc is not surjective:
ArcCsc is neither non-negative nor non-positive:
ArcCsc is neither convex nor concave:
Series Expansions (3)
Function Identities and Simplifications (3)
Branch cut of ArcCsc runs along the real axis:
Properties & Relations (4)
Use TrigToExp to express in terms of logarithm:
Use ExpToTrig to convert back:
Use FunctionExpand to convert trigs of arctrigs into an algebraic function:
Wolfram Research (1988), ArcCsc, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCsc.html (updated 2021).
Wolfram Language. 1988. "ArcCsc." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/ArcCsc.html.
Wolfram Language. (1988). ArcCsc. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCsc.html