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

1 Answer
Nov 30, 2016

Answer:

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]}