Which of the following functions have a vertical asymptote for values of Ø such that cos Ø = 1?Select all that apply.

Question

asked May 3, 2020 59.3k views

1 Answer

Paul Medcraft · Answer 1 · 2020-05-08T11:16:17+0000

Answer:

$y=\cot \theta$ and
$y=\csc \theta$

Explanation:

Note that if
$\cos \theta=1,$ then
$\sin \theta=0.$

Functions
$y=\cos \theta,\ \ y=\sin \theta$ do not have vertical asymptotes at all.

Vertical asymptotes have functions
$y=\tan \theta,\ \ y=\cot \theta,\ \ y=\sec \theta,\ \ y=\csc \theta.$

Functions
$y=\tan \theta$ and
$y=\sec \theta$ have the same vertical asymptotes (when
$\cos \theta =0$ ).

Functions
$y=\cot \theta$ and
$y=\csc \theta$ have the same vertical asymptotes (when
$\sin \theta =0$ ). See attached diagram