Question

Will Medal and Fan, please help?

Trig Question:
Need to find two vertical asymptotes for f(x) = - tan 4x?

I heard that you need to find values when cos(x)=0, but I don't know how to find x...

Answer 1

@sweetburger can you help please?

Answer 2

Do you know the unit circle?

Answer 3

hint:
the period of the function \(x \rightarrow -\tan x\) is \(T_0=\pi\), and its vertical asymptotes are located at \(x= \pm \pi/2, \pm 3\pi/2,...\)
Now the period of the function \(x \rightarrow -\tan (4x)\) is \(T_1=T_0/4\), so every value of \(x\) at which there is an asymptote for the function \(x \rightarrow -\tan x\) is reduced by a factor \(4\)

Answer 4

Refer to the attached plot.