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

`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