Question

Using the compound angle formulas, determine the exact value of Cos(11 pie/6)

Answer 1

@agent0smith

Answer 2

Cos(2theta) = 2sintheta. costheta

Answer 3

I'd use one of https://i.ytimg.com/vi/SMVExXdtXAI/maxresdefault.jpg
\[\large \cos ( x+y) = \cos x \cos y - \sin x \sin y\]Wait why do we need to use compound angle formulas... 11pi/6 can be done using reference angles alone.

Answer 4

because it says in the question to use the compound angle formula...

Answer 5

What an annoying question... why not give you an angle that'd make more sense to use it. I hate questions that make things pointlessly more difficult.
\[\Large \frac{ 11\pi }{ 6 } = \frac{ 6 \pi }{ 6 }+ \frac{ 5 \pi }{ 6 } = \pi +\frac{ 5 \pi }{ 6 } \]
\[\large \cos ( \pi+\frac{ 5 \pi }{ 6 }) = \cos \pi \cos \frac{ 5 \pi }{ 6 } - \sin \pi \sin \frac{ 5 \pi }{ 6 }\]

Answer 6

so do i have to find the related acute angle first and then use that in the formula or something?!?!?

Answer 7

btw sir i think you've used sum and difference idnentity and not double angle??!?1

Answer 8

"compound angle" doesn't specify which formula to use. It does not say to use double angle...

Easiest way would be this way, I guess
\[\Large \frac{ 11\pi }{ 6 } = \frac{ 12 \pi }{ 6 }- \frac{ \pi }{ 6 } = 2\pi -\frac{ \pi }{ 6 }\]
then use the formula from the link earlier
\[\large \cos ( 2\pi-\frac{ \pi }{ 6 }) = \cos 2\pi \cos \frac{ \pi }{ 6 } + \sin 2\pi \sin \frac{ \pi }{ 6 }=\]

Answer 9

oh sorry i thought it said double angle....g'sis sorry papa!!

Answer 10

ok thanks!!

Answer 11

I assume you can finish it from there?

Answer 12

btw how did you come up with 12 pei/6 and pie/6??

Answer 13

Because... \[\Large \frac{ 11 }{ 6} = \frac{ 12 }{ 6} - \frac{ 1 }{ 6} \]

Answer 14

no one has answered this simple question for me...before be use the compund angle formula, do we need to find the related acute angle first!?!?!?

Answer 15

No.

Answer 16

Well, sort of, you don't HAVE to, but it's easier.