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

Question

2555 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-30T10:49:38

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

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]}

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