Where does the graph of the function y is equal to tangent of x have asymptotes?

Since tan x = sin x / cos x, the function is undefined when cos x = 0. At those x-values, the graph has vertical asymptotes: x = π/2 + kπ, where k is any integer. Thus, the correct choice is where cosine of x is equal to 0.

AI-written and checked against the verified answer.