Question

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

sin 7 pi/8

Answer 1

\(\bf \cfrac{7}{8} \times 2 \implies \cfrac{7}{4}\\
sin\left(\frac{7 \pi}{8}\right) \implies sin\left(\cfrac{\frac{7 \pi}{4}}{2}\right)\)

Answer 2

and surely \(\bf \cfrac{7 \pi}{4}\) will be in your Unit Circle

Answer 3

would it be \[1/2\sqrt{2-\sqrt{2}}\]

Answer 4

as the final result

Answer 5

\(\bf sin\left(\cfrac{\frac{7 \pi}{4}}{2}\right) \implies
\sqrt{\cfrac{1-\left(-\frac{\sqrt{2}}{2}\right)}{2}}\\
\sqrt{\cfrac{1+\frac{\sqrt{2}}{2}}{2}} \implies
\sqrt{\cfrac{\frac{2+\sqrt{2}}{2}}{2}} \implies
\cfrac{\sqrt{2+\sqrt{2}}}{2}\)

Answer 6

Thats not an answer choices