Question

MEDAL REWARDED
Find the exact value by using a half-angle identity.
sin 7pi/8

Answer 1

@John_ES

Answer 2

Do you want the answer choices?

Answer 3

No needed. :)

Answer 4

First thing we must know is that,
\[\sin(7\pi/8)=\sin[(7\pi/4)/2]=-\sqrt{\frac{1}{2}(1-\cos(7\pi/4))}=-\sqrt{\frac{1}{2}(1-1/\sqrt{2})}\]
\[\sin(7\pi/8)=-\frac{\sqrt{2-\sqrt{2}}}{2}\]

Answer 5

Sorry, without the minus sign.

Answer 6

All my answer responses have 1/2 infront?

Answer 7

Yes, it should be,
\[\sin(7\pi/8)=\frac{1}{2}\sqrt{2-\sqrt{2}}\]