Question

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

sin(5pi/12)

Answer 1

@zzr0ck3r @SithsAndGiggles @surjithayer

Answer 2

fore warning, i don't know what half angle identity is

Answer 3

You'll find it here:
http://home.windstream.net/okrebs/page103.html

\(\huge sin(x)=\pm sqrt{\frac{(1-cos(2x))}{2}} \)

Answer 4

Set x=5pi/12, then 2x=10pi/12=5pi/6, and
cos(5pi/6)=cos(pi/6)=sqrt(3)/2
Take the positive value of sin(x) because sin(x)>0 for all 0<x<pi.

Answer 5

\[\sin \left( \frac{ 5\pi }{ 12 } \right)=\sqrt{\frac{ 1-\cos \left( \frac{ 5\pi }{ 6 } \right)}{ 2 }}\]
so it should look like this?

Answer 6

Yes.
Note that I made a mistake above.
cos(5pi/6)=-pi/6=-sqrt(3)/2
So that will change slightly if you decide to replace cos(5pi/6) by cos(pi/6).

Answer 7

\[\sin \left( \frac{ 5\pi }{ 12 } \right)=\sqrt{\frac{ 1-\cos \left( \frac{ \pi }{ 6 } \right) }{ 12 }}\]

Answer 8

that second 12 should be a 2