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Secant Function

Definition

Definition of the Secant Function

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

\sec \theta = \frac{\text{hypotenuse}}{\text{adjacent}}

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

Answer and Explanation(3 个标签)

secant functiondomainrange

Domain: $x \neq \frac{\pi}{2} + k\pi$ ; Range: $(-\infty, -1] \cup [1, +\infty)$ .

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

Answer and Explanation(3 个标签)

secant functionperiodparity

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

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

Chinese Term	English Term	Phonetic	Explanation
正割函数	secant function	/ˈsiːkənt ˈfʌŋkʃən/	One of the trigonometric functions, denoted as $\sec x$
正割	secant	/ˈsiːkənt/	Function name, abbreviated as $\sec$
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