Question

Which quadrants and axes does `f(x)=abs(tanx` pass through?

Answer 1

`f(x)>=0`. So, there is no crossing of its graph to the 3rd and 4th quadrants. It braces x-axis at two-tangent nodes `x=n pi, n=0, +-1, +-2, +-3...` As`xto(2n-1)pi/2, n=0,+-1,+-2,+-3.., ftooo`..

Explanation:

Interestingly, `|tanx|` is periodic with period `pi`, in contrast to the period `2pi`, for tan x.