Answer
$Period = 2\pi$
See below
Work Step by Step
If C is any real number and B > 0, then the graphs of $y = tan (Bx + C)$ and
$y = cot (Bx + C)$ will have
$Period = \frac{\pi}{B}$
$Horizontal\ shift = \frac{-C}{B}$
For equation $y = \frac{1}{3} \cot \frac{1}{2} x$
$Period = \frac{\pi}{\frac{1}{2}} = 2\pi$
Some values
$y = 0, at\ x = \pi$
$y = \frac{1}{3}\ at\ x = \frac{\pi}{2}$
$y = -\frac{1}{3}\ at\ x = \frac{3\pi}{2}$
$y -> \pm \infty\ at\ x = 0, 2\pi$
Using graph of $\cot x$ and above values one can plot the graph of $\frac{1}{3} \cot \frac{1}{2} x$
