Question

Which function's graph has asymptotes located at the values x = ind? v = escX II. y = cos III. y = tan x IV. y = cotx A. Il only O B. I and III only O c. 1only I OD. I and IV only SUBMIT

Answer 1

D. I and IV only

Step-by-step explanation:

You want to know which of the trig functions have asymptotes at x = nπ for integers n.

Vertical asymptotes

The trig functions with vertical asymptotes at x = nπ will be those that can be written equivalent to something with sin(x) in the denominator. Sin(x) is zero for x = nπ, so that will make 1/sin(x) have vertical asymptotes at those values of x.

I. csc(x) = 1/sin(x) . . . . . has vertical asymptotes at x=nπ

II. cos(x) . . . . is always finite; no asymptotes

III. tan(x) . . . . has vertical asymptotes an π/2+nπ

IV. cot(x) = cos(x)/sin(x) . . . . . has vertical asymptotes at x=nπ

The correct choice is I and IV only.