#### Answer

$\frac{2\pi}{3}$

#### Work Step by Step

$\sin s=\frac{\sqrt 3}{2}$ can be written as $s=\sin^{-1} (\frac{\sqrt 3}{2})$
Ensuring that the calculator is in radians, we type $\sin^{-1} (\frac{\sqrt 3}{2})$ into the calculator and solve:
$s=\sin^{-1} (\frac{\sqrt 3}{2})=\frac{\pi}{3}$
Since the interval is $[\frac{\pi}{2},\pi]$, we subtract the answer from $\pi$:
$\pi-\frac{\pi}{3}=\frac{2\pi}{3}$
Therefore, the exact value of $s$ in the interval $[\frac{\pi}{2},\pi]$ is $\frac{2\pi}{3}$.