Determine the exact value of the given trigonometric expression using the half-angle identity.
$\(\sin\]\frac{x}{2}\)$ if $\(\cos\) x=-\(\frac{17}{21}\)$ where $\(\frac{\pi}{2}\)<x<\(\pi\)$

• A. $\(\frac{\sqrt{399}\)}{21}$
• B. $-\(\frac{\sqrt{399}\)}{21}$
• C. $-\(\frac{\sqrt{798}\)}{21}$
• D. $\(\frac{\sqrt{798}\)}{21}$

Answer: (A)