Here's the question you clicked on:
mitchelsewbaran
Find the exact value by using a half-angle identity.
HINT: \(\large sin(x/2)=\pm \sqrt{\frac{1-cosx}{2}} \)
can you figure out what x = ??? first?
find x: \(\large \frac{7\pi}{8}=\frac{x}{2} \)
ok... so plugging that into the half angle formula: \(\large sin(\frac{7\pi}{8})=sin(\frac{\frac{7\pi}{4}}{2})=\pm \sqrt{\frac{1-cos(\frac{7\pi}{4})}{2}} \)
can you take it from here?