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

Nov 30, 2016

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

#### Explanation:

Note that:

$\cot \left(x - \frac{\pi}{2}\right) = \frac{\cos}{x - \frac{\pi}{2}} \sin \left(x - \frac{\pi}{2}\right) = - \frac{\cos}{\frac{\pi}{2} - x} \sin \left(\frac{\pi}{2} - x\right) = - \frac{\sin}{x} \cos x = - \tan x$

The range of $\tan x$ is $\left(- \infty , + \infty\right)$ 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]}