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Tangent Function

Definition

Definition of the Tangent Function

In a right triangle, let $\theta$ be an acute angle, then tangent is defined as:

\tan \theta = \frac{\text{opposite}}{\text{adjacent}}

where “opposite” refers to the side opposite to angle $\theta$ , and “adjacent” refers to the side adjacent to angle $\theta$ .

符号说明

Symbol	Type	Pronunciation/Explanation	Meaning in This Definition
$\theta$	Greek letter	Theta (theta)	Represents the measure of an angle (acute angle)

Find the domain and range of $y = \tan x$ .

Answer and Explanation(3 个标签)

tangent functiondomainrange

Domain: $x \neq \frac{\pi}{2} + k\pi$ ; Range: $\mathbb{R}$ .

Determine the periodicity and parity of $y = \tan x$ .

Answer and Explanation(3 个标签)

tangent functionperiodparity

Period is $\pi$ , it is an odd function.

Determine which of the following functions are trigonometric functions: $y = \sin x$ , $y = x^2$ , $y = \tan x$ , $y = e^x$ .

Answer and Explanation(3 个标签)

trigonometric functionsine functiontangent function

$y = \sin x$ , $y = \tan x$ are trigonometric functions, $y = x^2$ , $y = e^x$ are not.

Given $y = \tan x$ , write its domain and range.

Answer and Explanation(3 个标签)

tangent functiondomainrange

Domain: $x \neq \frac{\pi}{2} + k\pi$ ; Range: $\mathbb{R}$ .

Which of the following functions are odd functions?
(A) $y = \sin x$
(B) $y = \cos x$
(C) $y = \tan x$
(D) $y = x^2$

Answer and Explanation(5 个标签)

sine functioncosine functiontangent functionodd functioneven function

(A), (C) are odd functions, (B), (D) are not.

Given $y = \tan x$ , write its period and domain.

Answer and Explanation(3 个标签)

tangent functionperioddomain

Period is $\pi$ , domain is $x \neq \frac{\pi}{2} + k\pi$ .

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

Chinese Term	English Term	Phonetic	Explanation
正切函数	tangent function	/ˈtændʒənt ˈfʌŋkʃən/	One of the trigonometric functions, denoted as $\tan x$
正切	tangent	/ˈtændʒənt/	Function name, abbreviated as $\tan$
对边	opposite side	/ˈɒpəzɪt saɪd/	The right side opposite to the angle in a right triangle
邻边	adjacent side	/əˈdʒeɪsənt saɪd/	The right side adjacent to the angle in a right triangle
周期	period	/ˈpɪəriəd/	The smallest interval at which function values repeat
定义域	domain	/dəʊˈmeɪn/	The range of values for the independent variable