Answer
$sin~y = \sqrt{\frac{2}{3}}$
Work Step by Step
If $\frac{\pi}{2} \lt y \lt \pi$, then the angle $y$ is in quadrant II.
We can find the value of $sin~y$:
$sin~y = \sqrt{\frac{1-cos~2y}{2}}$
$sin~y = \sqrt{\frac{1-(-\frac{1}{3})}{2}}$
$sin~y = \sqrt{\frac{(\frac{4}{3})}{2}}$
$sin~y = \sqrt{\frac{2}{3}}$
