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gives the arc secant of the complex number .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • All results are given in radians.
  • For real outside the interval to , the results are always in the range to , excluding .
  • For certain special arguments, ArcSec automatically evaluates to exact values.
  • ArcSec can be evaluated to arbitrary numerical precision.
  • ArcSec automatically threads over lists.
  • ArcSec[z] has a branch cut discontinuity in the complex plane running from to .
Result in radians:
Series expansion:
Result in radians:
Click for copyable input
Click for copyable input
Series expansion:
Click for copyable input
Evaluate numerically:
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
TraditionalForm formatting:
ArcSec can deal with real-valued intervals:
Infinite arguments give symbolic results:
ArcSec can be applied to power series:
Find series expansions at branch points and branch cuts:
ArcSec threads over explicit lists as well as over sparse arrays:
Branch cut of ArcSec runs along the real axis:
Compose with inverse functions:
Use PowerExpand to disregard multivaluedness of the ArcSec:
Alternatively, evaluate under additional assumptions:
Use TrigToExp to express in terms of logarithm:
Use ExpToTrig to convert back:
Use FunctionExpand to convert trigs of arctrigs into an algebraic function:
Simplify result:
Use Reduce to solve equations involving ArcSec:
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