Question

Find the exact value by using a half-angle identity.

Answer 1

HINT: \(\large sin(x/2)=\pm \sqrt{\frac{1-cosx}{2}} \)

Answer 2

can you figure out what x = ??? first?

Answer 3

find x: \(\large \frac{7\pi}{8}=\frac{x}{2} \)

Answer 4

i got 7pi/4

Answer 5

ok... so plugging that into the half angle formula:
\(\large sin(\frac{7\pi}{8})=sin(\frac{\frac{7\pi}{4}}{2})=\pm \sqrt{\frac{1-cos(\frac{7\pi}{4})}{2}} \)

Answer 6

can you take it from here?