Question

Where does the graph of the function y=tan(x) have asymptotes?

Answer 1

The graph of y = tan x has vertical asymptotes at x = π/2 and x = –π/2,. The period of the tangent function is π, vertical asymptotes also occur when x = π/2 + nπ, where n is an integer.

Answer 2

Answer:

the asymptotes of graph y=tan(x) occur at  $\frac{pi}{2}+n\pi$

Step-by-step explanation:

The graph  of y=tan(x) is shown in figure-1

$tan\,x=\frac{sin\,x}{cos\,x}$

so, the vertical asymptotes occur when dinominator is zero

cos x = 0

$0=cos(\frac{pi}{2}) = cos(\frac{pi}{2}+n\pi)$

The vertical asymptotes occur at x=$\frac{pi}{2}+n\pi$

where n is an integer.

Hence, the asymptotes of graph y=tan(x) occur at  $\frac{pi}{2}+n\pi$