Answer
$Period = 1$
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 $y = -\cot \pi x$
$Period = \frac{\pi}{\pi} = 1$
The graph will be inverted due to minus sign
Some values
$y = 0, at\ x = \frac{1}{2}$
$y = 1\ at\ x = \frac{3}{4}$
$y = -1\ at\ x = \frac{1}{4}$
$y -> \pm \infty\ at\ x = 0, 1$
Using graph of $\cot x$ and above values one can plot the graph of $-\cot \pi x$
