find the vertical asymptote of f (x)= tan (-3x)

Question

my instructor says the answer is 2k + 1/x ( π ) , k= 0, +/- 1, etc.

I don't understand how he got that.

Answer 1

tan(θ) = sin(θ)/cos(θ)

There is an asymptote where cos(θ) = 0 or θ = π/2 + kπ = -3x

-3x = π(1/2+k)

x = -π/3(1/2+k)= -π/6(1+ 2k) = -(2k+1)/6)π

Are you sure you copied his answer correctly? If you plot tan(-3x) and (2k+1) multiples of -π/6 then you see all the asymptotes.