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Arcsecant Function

Definition

Definition of the Arcsecant Function

The arcsecant function $y = \operatorname{arcsec} x$ is the inverse function of the secant function $y = \sec x$ .

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

Answer and Explanation

arcsecant functiondomainrange

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

Symbol	Type	Pronunciation/Explanation	Meaning in This Article
$\pi$	Greek letter	Pi (pie)	Pi, used to represent the range of the arcsecant function

Chinese Term	English Term	Phonetic	Explanation
反正割函数	arcsecant function	/ɑːkˈsiːkənt ˈfʌŋkʃən/	The inverse function of the secant function, denoted as $y = \arcsec x$
反正割	arcsecant	/ɑːkˈsiːkənt/	Function name, abbreviated as $\arcsec$
反函数	inverse function	/ɪnˈvɜːs ˈfʌŋkʃən/	A function that is the inverse of the original function
定义域	domain	/dəʊˈmeɪn/	The range of values for the independent variable
值域	range	/reɪndʒ/	The range of values for the function