Question

Find the exact value.

Answer 1

\[\sin \frac{ 5\pi }{ 8 }\]

Answer 2

Use the sin half angle identity.
sin(x/2)=\[\sqrt{(1-cosx)/2}\]
If x/2=5π/8 then x=5π/4
Plug this into the half angle identity to get \[\sqrt{(1-cos(5π/4))/2}\]
This simplifies to \[\sqrt{(2-√2)/4}\] and then into √(2-√2)/2

Answer 3

Just to clarify, the negative square root is discarded because 5π/8 is in Q2 so sinx has to be positive.

Answer 4

thanks so much!