# How do you graph y=-tan(x-pi/2)?

Aug 12, 2018

See explanation and graph.

#### Explanation:

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

$x \ne$ ( asymptotic zero of the denominator sin x ) $k \pi$,

$k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$.

The period is the period of tan x $= \pi$

Axis: y = 0

Amplitude for infinite wave length = 1/2 (space between two

consecutive asymptotes $= \frac{\pi}{2}$

See graph, depicting all these aspects.

graph{(y sin x - cos x)(y+0x)(x+0y)(x-pi+0y)(x+pi+0y) = 0}