Answer
Vertical asymptotes at the values $t$ such that $t=\pi k$ where k is a non-zero integer.
Work Step by Step
$s(t)=\dfrac{t}{\sin{t}}$.
Vertical asymptotes occur when the denominator alone is $0\to$
$\sin{t}=0\to t=\pi k$ where k is a non-zero integer.
Note: The reason $k=0$ is excluded is because it makes both the numerator and denominator $0.$
