Question

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

Answer 1

Type out the "half-angle identity" for the cosine function, please.

Answer 2

Think: \[\frac{ 5\pi }{ 12 }\]

Answer 3

...is half of what angle?

Answer 4

10Pi

Answer 5

5pi/12 is half as large as 5pi/6
So we can do something clever :)
\[\large\rm \cos\left(\frac{5\pi}{12}\right)=\cos\left(\frac{\color{orangered}{5\pi/6}}{2}\right)\]

Answer 6

And then you remember your Half-Angle Identity, yes?\[\large\rm \cos\left(\frac{\color{orangered}{x}}{2}\right)=\sqrt{\frac{1+\cos\color{orangered}{x}}{2}}\]

Answer 7

yes

Answer 8

i got to there but I can't come up with an answer

Answer 9

@zepdrix