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Inverse Cosecant Function

Definition

Definition of Inverse Cosecant Function

The inverse cosecant function y=arccsc⁡xy = \operatorname{arccsc} x is the inverse function of the cosecant function y=csc⁡xy = \csc x.

符号说明
SymbolTypePronunciation/NoteMeaning in this article
π\piGreek letterPi (pie)Pi, used to represent the range of the inverse cosecant function

Properties

  • Domain: (−∞,−1]∪[1,+∞)(-\infty, -1] \cup [1, +\infty)
  • Range: [−π2,0)∪(0,π2][-\frac{\pi}{2}, 0) \cup (0, \frac{\pi}{2}]
  • Monotonicity: Decreasing on its domain

Graph

Exercises

Exercise 1

Given y=arccsc⁡xy = \operatorname{arccsc} x, find its domain and range.

Answer and Analysis (3 个标签)
inverse cosecant function domain range

Domain: (−∞,−1]∪[1,+∞)(-\infty, -1] \cup [1, +\infty); Range: [−π2,0)∪(0,π2][-\frac{\pi}{2}, 0) \cup (0, \frac{\pi}{2}].

Summary

Symbols Used in This Article

SymbolTypePronunciation/NoteMeaning in this article
π\piGreek letterPi (pie)Pi, used to represent the range of the inverse cosecant function

Bilingual Glossary

Chinese TermEnglish TermPhoneticExplanation
反余割函数inverse cosecant function/ɪnˈvɜːrs koʊˈsiːkənt ˈfʌŋkʃən/The inverse function of the cosecant function, denoted as y=arccsc⁡xy = \operatorname{arccsc} x
反余割inverse cosecant/ɪnˈvɜːrs koʊˈsiːkənt/Function name, abbreviated as arccsc⁡\operatorname{arccsc}
反函数inverse function/ɪnˈvɜːs ˈfʌŋkʃən/A function that reverses another function
定义域domain/doʊˈmeɪn/The set of input values for which the function is defined
值域range/reɪndʒ/The set of output values of the function
Previous Arcsecant Function Detailed explanation of the arcsecant function's definition, properties, graph, and typical exercises.
Next The Mathematical Adventure of Natural Constant e From Bernoulli's compound interest problem to Euler's great discovery, explore the history, definition, properties, and applications of the natural constant e.

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