Answer
$\color{blue}{s=\dfrac{11\pi}{6}}$
Work Step by Step
Note that $\dfrac{\pi}{6}$ is a special angle and $\sin{(\dfrac{\pi}{6})}=\frac{1}{2}$.
RECALL:
An angle and its reference angle have either the same trigonometric values or they differ only in signs.
Since $s$ must be in $\left[\dfrac{3\pi}{2}, 2\pi\right]$, then the angle must terminate in Quadrant IV.
Note that the angle of $\dfrac{11\pi}{6}$ is in Quadrant IV and its reference angle is $\dfrac{\pi}{6}$.
Sine is negative in Quadrant IV.
Thus,
$\sin{(\frac{11\pi}{6})} = -\frac{1}{2}$
Therefore, if $\sin{s} = -\frac{1}{2}$ and $s$ is in $\left[\dfrac{3\pi}{2}, 2\pi\right]$, then $\color{blue}{s=\dfrac{11\pi}{6}}$.
