Question

Find the exact value by using a half-angle identity.
tan7π/8

PLEASE PLEASE PLEASE :)

Answer 1

Well, the half angle identity says: \[
\sin(\theta/2) = \sqrt{\frac{1-\cos(\theta)}{2}} \quad \cos(\theta/2) = \sqrt{\frac{1+\cos(\theta)}{2}}
\]

Answer 2

but what about tan..

Answer 3

Well \[
\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}
\]So I didn't really remember it's identity for this. Rather, I just divided the other identities.

Answer 4

So then \[
\tan(\theta / 2) = \sqrt{\frac{1-\cos(\theta)}{1+\cos(\theta)}}
\]

Answer 5

well i just don't really understand how to do the problem once everything is plugged in

Answer 6

Well, \(\cos(7\pi/4)\) is relatively easy to solve for, when you look at the unit circle.

Answer 7

well i know how to find the degree but once i get the degree i dont know where to go from there

Answer 8

that is a good method... but tan's identity is below
\[\large \tan (\frac{ \theta }{ 2 }) =\frac{ \sin(\theta) }{1+ \cos (\theta) }=\frac{ 1- \cos (\theta) }{\sin(\theta) }\]

Answer 9

do you mind just showing me the steps please??