# How do you graph y=3cot(1/2x)-2?

Aug 11, 2018

See explanation and graph.

#### Explanation:

#y = 3 cot (x/2) - 2,

$x \ne$( asymptotic zero of the denominator sin (x/2) ) $2 k \pi$,

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

The period is the period of $\tan \left(\frac{x}{2}\right) = \frac{\pi}{\frac{1}{2}} = 2 \pi$.

Vertical shift for the axis is $-$, and so, the axis is

$y = - 2$.

See graph, depicting all these aspects.
graph{((y+2)sin (x/2) - cos (x/2))(y+2+0x)(x-2pi+0.0001y)(x+2pi+0.0001y)(x+0.0001y) = 0[-20 20 -12 8] }