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Arcsine Function

Definition

Definition of the Arcsine Function

The arcsine function $y = \arcsin x$ is the inverse function of the sine function $y = \sin x$ .

Given $y = \arcsin x$ , find its domain and range.

Answer and Explanation (3 个标签)

arcsine function domain range

Domain: $[-1, 1]$ ; Range: $[-\frac{\pi}{2}, \frac{\pi}{2}]$ .

Symbol	Type	Pronunciation/Explanation	Meaning in This Article
$\pi$	Greek letter	Pi (pie)	Pi, used to represent the range of the arcsine function $([-\frac{\pi}{2}, \frac{\pi}{2}])$

Chinese Term	English Term	Phonetic	Explanation
反正弦函数	arcsine function	/ɑːkˈsaɪn ˈfʌŋkʃən/	The inverse function of the sine function, denoted as $y = \arcsin x$
反正弦	arcsine	/ɑːkˈsaɪn/	Function name, abbreviated as $\arcsin$
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
奇函数	odd function	/ɒd ˈfʌŋkʃən/	A function satisfying $f(-x) = -f(x)$

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