Question

For what values of t on the interval [2pie, 2pie] does the graph of h(t) = tan t have vertical asymptotes?

Answer 1

From the graph of tan t, it will have vertical asymptotes at
t = -3pi/2, -pi/2, pi/2, 3pi/2

Answer 2

at 4 places on the closed interval [ - 2pi, 2 pi]

Answer 3

You'll want where tanx is undefined... tan x is \[\Large \frac{ \sin x }{\cos x }\]it's undefined where cosx = 0 since that means dividing by zero. Can you find where cosx=0? (between -2pi and 2pi)

Answer 4

Cosx = 0 for \[\Large x = \frac{ \pi }{ 2 } \pm \pi\]

Answer 5

x = pi/2 +/- n pi, where n is an integer

Answer 6

Yeah, i forgot the k or n, oops