Question

Find the exact value by using a half-angle identity. Sin(7pi/8)

Answer 1

ok so the half angle identity for sin is.....\[\sin \frac{ x }{ 2 }=\sqrt{(1-cosx)/2}\]
so \[\sqrt{(1-\cos7\pi)/8} \]\[\sqrt{(1/4)}\sqrt{(1-\cos7\pi)/2}\]
we end up with \[\frac{ 1 }{ 2 }*\sqrt{(1-(-1))/2}\]
\[\frac{ 1 }{ 2 }*\sqrt{(1+1)/2}\]
\[\frac{ 1 }{ 2 }*\sqrt{1}\] ok u can finish it from there?

Answer 2

so did u get the answer?

Answer 3

\[\pm \frac{ 1 }{ 2 }\]