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Cotangent Function

Definition

Definition of the Cotangent Function

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

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

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

Answer and Explanation(3 个标签)

cotangent functiondomainrange

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

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

Answer and Explanation(3 个标签)

cotangent functionperiodparity

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

【2018·Mathematics 3】Which of the following functions are odd functions? (A) $y = \sin x$ (B) $y = \cos x$ (C) $y = \cot x$ (D) $y = x^2$

Answer and Explanation(5 个标签)

sine functioncosine functioncotangent functionodd functioneven function

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

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

Chinese Term	English Term	Phonetic	Explanation
余切函数	cotangent function	/kəʊˈtændʒənt ˈfʌŋkʃən/	One of the trigonometric functions, denoted as $\cot x$
余切	cotangent	/kəʊˈtændʒənt/	Function name, abbreviated as $\cot$
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