Question

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

Answer 1

Answer:

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

Step-by-step 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