Question

Find the exact value by using a half-angle identity.
sin7pi/8

I got 1/2squareroot2-squareroot2 but idk if it's right!

Answer 1

\[\sin(\frac{ x }{ 2 }) = \sqrt{\frac{ 1-cosx }{ 2 }}\]In your case, your x would be 7pi/4. And cos(7pi/4) = sqrt(2)/2 So that means:

\[\sqrt{\frac{ 1-\frac{ \sqrt{2} }{ 2 } }{ 2 }}\implies \sqrt{\frac{ \frac{ 2-\sqrt{2} }{ 2 } }{ 2 }}\implies \sqrt{\frac{ 2-\sqrt{2} }{ 4 }}=\frac{ 1 }{ 2 }*\sqrt{2-\sqrt{2}}\]Which Im guessing is what you meant xD

Answer 2

Yeahh! Omg thanks for explaining it! I wasn't entirely sure if I did the process right. Thanks again!!

Answer 3

Yep, np ^_^