Question

The exact value of cos 5pi/12 is:

sqrt 2 (sqrt 3+1) / 4

sqrt 2 (sqrt 3-1) / 4

0.26

0.99

Answer 1

\[\cos(\frac{5\pi}{12})=\cos(\frac{1}{2} \cdot \frac{ 5\pi}{6})\]
halfangle formula comes in mind

Answer 2

@freckles i got\[\frac{ \sqrt{6}-\sqrt{2} }{ 4 }\] i doesnt match any of the answers that im supposed to get

Answer 3

woah how did you get that!

Answer 4

\[\cos^2(\frac{a}{2})=\frac{1+\cos(a)}{2}\]
this was the half angle formula

Answer 5

our a here is 5pi/6

Answer 6

5pi/12 is in the first quadrant
so when we take square root of both sides we know to use the + instead of the -
since cos is positive in the first quadrant

Answer 7

0.25881905 that was what i got when i put it into my calculator

Answer 8

\[\cos(\frac{a}{2})=\sqrt{\frac{1+\cos(a)}{2}}\]

Answer 9

do you know what cos(5pi/6) is?

Answer 10

yes - sqrt 3/2

Answer 11

\[\cos(\frac{1}{2} \cdot \frac{5\pi}{6})=\sqrt{\frac{1+\frac{-\sqrt{3}}{2}}{2}}\]

Answer 12

now we have an ugly compound fraction inside that sqrt( )

Answer 13

oh so its a?

Answer 14

so inside multiply top and bottom by 2

Answer 15

\[\cos(\frac{1}{2} \cdot \frac{5\pi}{6})=\sqrt{\frac{2}{2} \cdot \frac{1+\frac{-\sqrt{3}}{2}}{2}} \]