Question

How do you graph, identify the domain, range, and asymptotes for `y=cot(x-pi/2)`?

Answer 1

They are the same as the ones for `y=tan x`

Explanation:

Note that:

`cot(x-pi/2) = frac cos (x-pi/2) sin (x-pi/2) = - frac cos( pi/2-x) sin(pi/2-x) = - frac sinx cosx = -tan x`

The range of `tan x` is `(-oo,+oo)` so it is not affected by the change in sign.

Same for the domain of `tan x` that is symmetrical with respect to `x=0`

Also the asymptotes do not change, only the approach to the asymptotes is reversed.

graph{cot(x-pi/2) [-10, 10, -5, 5]}