Question

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

cosine of five pi divided by twelve.

Answer 1

\[\frac{5\pi}{12}\]is half of \(\frac{5\pi}{6}\)

Answer 2

so
\[\cos(\frac{5pi}{12})=\sqrt{\frac{1+\cos(\frac{5\pi}{6})}{2}}\]

Answer 3

that's my final answer?

Answer 4

lol no

Answer 5

your final answer should be a number
find \(\cos(\frac{5\pi}{6})\) and plug it in

Answer 6

\[\cos(\frac{5\pi}{6})=\frac{\sqrt3}{2}\] so you will have to do a bit of work to make that look reasonable

Answer 7

oops my mistake \[\cos(\frac{5\pi}{6})=-\frac{\sqrt3}{2}\]

Answer 8

\[\cos(\frac{5\pi}{12})=\sqrt{\frac{1-\frac{\sqrt3}{2}}{2}}\]

Answer 9

more simplified
\[\cos(\frac{5\pi}{12})=\frac{\sqrt{2-\sqrt{3}}}{2}\]

Answer 10

Thank you!!

Answer 11

welcome!

Answer 12

well thank @satellite73 though :)

Answer 13

Soory, Thank you to each person for trying to help someone who knows nothing! You are both amazing!(:

Answer 14

haha welcome in place of everyone ^_^