Answer:
[tex]y=\cot \theta[/tex] and [tex]y=\csc \theta[/tex]
Step-by-step explanation:
Note that if [tex]\cos \theta=1,[/tex] then [tex]\sin \theta=0.[/tex]
Functions [tex]y=\cos \theta,\ \ y=\sin \theta[/tex] do not have vertical asymptotes at all.
Vertical asymptotes have functions [tex]y=\tan \theta,\ \ y=\cot \theta,\ \ y=\sec \theta,\ \ y=\csc \theta.[/tex]
Functions [tex]y=\tan \theta[/tex] and [tex]y=\sec \theta[/tex] have the same vertical asymptotes (when [tex]\cos \theta =0[/tex]).
Functions [tex]y=\cot \theta[/tex] and [tex]y=\csc \theta[/tex] have the same vertical asymptotes (when [tex]\sin \theta =0[/tex]). See attached diagram
