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

Jan 2, 2017

It is periodic, with period $\frac{\pi}{2}$. The graph is for ${12}_{+}$ periods.
I am satisfied that this edition is bug-free.

#### Explanation:

For $\cot \left(2 x + \frac{\pi}{3}\right) + 1$, the period is $\frac{\pi}{2}$. The asymptotes are given by

$2 x + \frac{\pi}{3}$= a multiple of $\pi = k \pi$, giving $x = \frac{k \pi - \frac{\pi}{3}}{2} = \left(\frac{3 k - 1}{6}\right) \pi , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

For one period, $x \in \left(- \frac{\pi}{6} , \frac{\pi}{3}\right)$,

there are two terminal asymptotes

$\uparrow x = - \frac{\pi}{6} \downarrow \mathmr{and} \uparrow x = \frac{\pi}{3} \downarrow$.

graph{(y-1)tan(2x+1.047)-1=0 [-10, 10, -5.21, 5.21]}