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Inverse Cosecant Function

Definition

Definition of Inverse Cosecant Function

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

Symbol	Type	Pronunciation/Note	Meaning in this article
$\pi$	Greek letter	Pi (pie)	Pi, used to represent the range of the inverse cosecant function

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

Answer and Analysis

inverse cosecant functiondomainrange

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

Symbol	Type	Pronunciation/Note	Meaning in this article
$\pi$	Greek letter	Pi (pie)	Pi, used to represent the range of the inverse cosecant function

Chinese Term	English Term	Phonetic	Explanation
反余割函数	inverse cosecant function	/ɪnˈvɜːrs koʊˈsiːkənt ˈfʌŋkʃən/	The inverse function of the cosecant function, denoted as $y = \operatorname{arccsc} x$
反余割	inverse cosecant	/ɪnˈvɜːrs koʊˈsiːkənt/	Function name, abbreviated as $\operatorname{arccsc}$
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