Answer
Vertical asymptotes at every integer value of $x.$
Work Step by Step
A function has vertical asymptotes at values that make only the denominator $0$.
$f(x)=\csc{\pi x}=\dfrac{1}{\sin{\pi x}}\to \sin{\pi x}=0 \to \pi x=\pi k\to x=k$ where $k$ is any integer.
