Question

Which of the following functions have a vertical asymptote for values of theta such that cos theta = 1? Select two answers.

y = sin theta
y = cos theta
y = tan theta
y = sec theta
y = csc theta
y = cot theta

Answer 1

The sine is zero at such angles, so
.. y = csc(θ)
.. y = cot(θ)
both have vertical asymptotes there.

The last 2 selections.

Answer 2

cos(θ) = 1

sin(θ) =
`√(1-cos^2) =√(1-1^2) = 0`

sin(θ)=0

It means θ = 0 , 360

y= sin(θ) , it does not has any Vertical Asymptote

y=cos(θ), it also does not has any vertical Asymptote

y= tan(θ) , It does not has Vertical Asymptote at 0 and 360.

y = sec(θ) , it does not has vertical asymptote at 0 and 360 .

y=csc(θ) , it has vertical asymptote at 0 and 360

y= cot(θ) , it also has vertical asymptote at 0 and 360.