Question

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

a.) y = sin θ
b.) y = cos θ
c.) y = tan θ
d.) y = sec θ
e.) y = csc θ
f.) y = cot θ

Answer 1

Well costheta=1, at 0, 2pi,...
knowing this we can exclude the first two as the are not undefined anywhere.
tan is sin/cos, at 0 sin is also 0 so it becomes 0/1 which is 0, not undefined.
sec is1/cos, cos is 1, this is just 1
csc is 1/sin, sin is 0, 1/0 is undefined, meaning there will be an asymptote
cot is cos/sin, this is again 1/0, so it is also an asymptote
The last two answers are the ones you want