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Arctangent Function

Definition

Definition of the Arctangent Function

The arctangent function $y = \arctan x$ is the inverse function of the tangent function $y = \tan x$ .

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

Answer and Explanation (3 个标签)

arctangent function domain range

Domain: $\mathbb{R}$ ; 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 arctangent function $((-\frac{\pi}{2}, \frac{\pi}{2}))$

Chinese Term	English Term	Phonetic	Explanation
反正切函数	arctangent function	/ɑːkˈtændʒənt ˈfʌŋkʃən/	The inverse function of the tangent function, denoted as $y = \arctan x$
反正切	arctangent	/ɑːkˈtændʒənt/	Function name, abbreviated as $\arctan$
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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Exploring Functions in Advanced Mathematics
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Functions are a core idea of advanced mathematics. This course walks through foundational concepts, key properties, and classic constants so you can read, reason, and compute with confidence.
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