Question

Which of the following is an asymptote of y = csc(x)? Thank you!

Answer 1

The asymptote of the function $y = \csc \left( x \right)$ is $\boxed{x = - \pi }.$

Further explanation:

Given:

The function is $y = \csc \left( x \right)$

The options are as follows,

(a).$x = - \pi$

(b).$x =- \dfrac{\pi }{3}$

(c).$x =\dfrac{\pi }{4}$

(d).$x=\dfrac{\pi }{2}$

Explanation:

The vertical asymptote is point at which the function is not defined.

The value of $y = \csc \left( x \right)$ can be written as follows,

$y=\csc\left( x \right)=\dfrac{1}{{\sin \left( x \right)}}$

The function is not defined if the value of \sin \left( x \right) = 0.

The value of $\sin \left( x \right) = 0 at x = 0 or x = n\pi.$

The value of $y = \dfrac{1}{{\sin \left( x \right)}}$ is not defined for $x = - \pi.$

The asymptote of the function $y = \csc \left( x \right)$ is $\boxed{x = - \pi }.$

Option (a) is correct as the asymptote of the function is $x = - \pi.$

Option (b) is not correct as the asymptote of the function is $x = - \pi.$

Option (c) is not correct as the asymptote of the function is $x = - \pi.$

Option (d) is not correct as the asymptote of the function is $x = - \pi.$

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 brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: asymptote, y=cos(x), vertical asymptote, horizontal asymptote.

Answer 2

Vertical asymptotes appear at any n*pi with n as some integer
in your case x=-1*pi (the others are fractions not integers), so the first option