The asymptote of the function [tex]y = \csc \left( x \right)[/tex] is [tex]\boxed{x = - \pi }.[/tex]
Further explanation:
Given:
The function is [tex]y = \csc \left( x \right)[/tex]
The options are as follows,
(a).[tex]x = - \pi[/tex]
(b).[tex]x =- \dfrac{\pi }{3}[/tex]
(c).[tex]x =\dfrac{\pi }{4}[/tex]
(d).[tex]x=\dfrac{\pi }{2}[/tex]
Explanation:
The vertical asymptote is point at which the function is not defined.
The value of [tex]y = \csc \left( x \right)[/tex] can be written as follows,
[tex]y=\csc\left( x \right)=\dfrac{1}{{\sin \left( x \right)}}[/tex]
The function is not defined if the value of \sin \left( x \right) = 0.
The value of [tex]\sin \left( x \right) = 0 at x = 0 or x = n\pi.[/tex]
The value of [tex]y = \dfrac{1}{{\sin \left( x \right)}}[/tex] is not defined for [tex]x = - \pi.[/tex]
The asymptote of the function [tex]y = \csc \left( x \right)[/tex] is [tex]\boxed{x = - \pi }.[/tex]
Option (a) is correct as the asymptote of the function is [tex]x = - \pi.[/tex]
Option (b) is not correct as the asymptote of the function is [tex]x = - \pi.[/tex]
Option (c) is not correct as the asymptote of the function is [tex]x = - \pi.[/tex]
Option (d) is not correct as the asymptote of the function is [tex]x = - \pi.[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Trigonometry
Keywords: asymptote, y=cos(x), vertical asymptote, horizontal asymptote.
