Answer
$s=0$
Work Step by Step
We are given the function:
$q(s)=\dfrac{\pi}{s-\sin s}$
We should compute $\lim\limits_{s \to a} q(s)=\lim\limits_{s \to a}\dfrac{\pi}{s-\sin s}$
The function $q(s)$ is undefined for $s-\sin s=0$.
$s=\sin s$
$\sin s\in[-1,1]$
On the interval $[-1,1]$, $y=s$ is ascending, while $y=\sin s$ is also ascending. They intersect in $s=0$. As they are bot ascending functions, $s=0$ is the only intersection.
Therefore $q(s)$ has one vertical asymptote in $s=0$.
