Question

Find the exact value of cos (5pi/12) by using a half-angle identity. 

Answer 1

HI!!

Answer 2

\[\frac{5\pi}{12}\] is half of \[\frac{5\pi}{6}\] use that one !!

Answer 3

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

Answer 4

Hi misty 1212 :) Thanks for replying
I know the formula is cos (a/2) = ±√(1 + cos a)/2
but I don't know what to do next

Answer 5

compute the number is all that is left to do

Answer 6

id you see the answer i wrote above?
it was with \(\frac{a}{2}=\frac{5\pi}{12}\) and \(a=\frac{5\pi}{6}\)

Answer 7

did i lose you somewheres?

Answer 8

OK yea so would that be cos(5 pi/6) = -sqrt(3)/2?

Answer 9

at this point what you need to do is find
\[\cos(\frac{5\pi}{6})\] and plug it in above

Answer 10

yes that is right

Answer 11

\[\cos(\frac{5\pi}{12})=\sqrt{\frac{1+\cos(\frac{5\pi}{6})}{2}}=\sqrt{\frac{1-\frac{\sqrt3}{2}}{2}}\]

Answer 12

you can simplify that compound fraction by multiplying inside the radical top and bottom by 2

Answer 13

oh i should add that there is a plus or minus outside in the formula, but the answer is positive in this case because you are in quadrant 1

Answer 14

\[2 \cos ^2\frac{ 5 \pi }{ 12 }=1+\cos \frac{ 5 \pi }{ 6 }=1+\cos \left( \pi-\frac{ \pi }{ 6 } \right)=1-\cos \frac{ \pi }{ 6 }=1-\frac{ \sqrt{3} }{ 2 }\]
\[\cos \frac{ 5 \pi }{ 12 }=\sqrt{\frac{ 2-\sqrt{3} }{ 4 }}=\frac{ \sqrt{2-\sqrt{3}} }{ 2 }\]

Answer 15

cos (5 pi/12) = sqrt( ( (2-sqrt(3))/4 ) )
Would that be the final answer ?

Answer 16

yes, but not really because you know that the square root of four is two

Answer 17

so you would probably write
\[\frac{\sqrt{2-\sqrt3}}{2}\]

Answer 18

Oh so the final answer is 1/2 ?

Answer 19

oh no !!
the final answer is what i wrote above

Answer 20

Oh lol I thought I had to simplify it

Answer 21

Thank you so much misty1212 This Really helped me a lot!! :D