Answer
$Period = 2$
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 $y = \frac{1}{2} \cot \frac{\pi}{2} x$
$Period = \frac{\pi}{\frac{\pi}{2}} = 2$
Some values
$y = 0, at\ x = 1$
$y = \frac{1}{2}\ at\ x = \frac{1}{2}$
$y = -\frac{1}{2}\ at\ x = \frac{3}{2}$
$y -> \pm \infty\ at\ x = 0, 2$
Using graph of $\cot x$ and above values one can plot the graph of $\frac{1}{2} \cot \frac{\pi}{2} x$
