Question

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

sin(7pi/8)

Answer 1

Would I be using the formula: \[\sin \frac{ x }{ 2 }=\pm \sqrt{\frac{ 1+cosx }{ 2 }}\]

Answer 2

http://www.mathplanet.com/images/math/codecogs_2b7e3598.gif

Answer 3

What exactly does that mean?

Answer 4

hmmm what ?

Answer 5

Those are half-angle formulas for sine and cosine. I don't understand what you're trying to imply.

Answer 6

ohhh that's what you'd be using, is a -cos, not a +cos like you post it

anyhow... \(\bf \cfrac{7}{8}\cdot 2\implies \cfrac{7}{4}\qquad \cfrac{7\pi}{8}\cdot 2\implies \cfrac{7\pi}{4}\\ \quad \\

sin\left(\frac{7\pi}{8}\right)\implies sin\left(\cfrac{\frac{7\pi}{4}}{2}\right)=\pm \sqrt{\cfrac{1-cos\left(\frac{7\pi}{4}\right)}{2}}\)

Answer 7

and you can find \(\bf \cfrac{7\pi}{4}\) in your Unit Circle

Answer 8

Oh, yeah sorry it was a typo! Thank you!

Answer 9

yw