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Cosecant Function

Definition

Definition of the Cosecant Function

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

\csc \theta = \frac{\text{hypotenuse}}{\text{opposite}}

where “hypotenuse” is the longest side of the triangle, 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 $y = \csc x$ .

Answer and Explanation(3 个标签)

cosecant functiondomainrange

Domain: $x \neq k\pi$ ; Range: $(-\infty, -1] \cup [1, +\infty)$ .

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

Answer and Explanation(3 个标签)

cosecant functionperiodparity

Period is $2\pi$ , it is an odd function.

Symbol	Type	Pronunciation/Explanation	Meaning in This Article
$\pi$	Greek letter	Pi (pie)	Pi, used to represent the period of the cosecant function ( $2\pi$ )

Chinese Term	English Term	Phonetic	Explanation
余割函数	cosecant function	/kəʊˈsiːkənt ˈfʌŋkʃən/	One of the trigonometric functions, denoted as $\csc x$
余割	cosecant	/kəʊˈsiːkənt/	Function name, abbreviated as $\csc$
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