Question

Could someone please explain how to find an exact value of sin(11pi/12)? I'm not sure how to get them in the answer as the ones given:
A. (Sq. Rt 2 - Sq. Rt 6)/4
B. (/Sq. Rt 6 - Sq. Rt 2)/4
C. (Sq. Rt 6 - Sq. Rt 2)/4
D. (Sq. Rt 6 + Sq. Rt 2)/4

Answer 1

11pi/12 is half of 11pi/6, so you can use a half angle identity.
\[\sin \frac{ \theta }{ 2 }=\sqrt{\frac{ 1-\cos \theta }{ 2 }}\]
where Θ=11π/6

Answer 2

Ok, but how can I get the answers like the ones I was given?

Answer 3

Because I simplified the problem to: 2pi/3 + pi/4. But I'm not sure how to get them simplified to what answers I am given.

Answer 4

you used a different identity, so you got the answer in a different format. The easiest way to get the answer in the root of a root format is to use the half angle identity

Answer 5

actually hold up

Answer 6

ok so you used the \(\sin(a + b) = \sin a \cos b + \cos a \sin b \) identity?

Answer 7

Yes, I think so.

Answer 8

what did you get when you did it?

Answer 9

Well, I only have right now, 2pi/3 + pi/4

Answer 10

you have to substitute the values you got into the equation and evaluate it\[\sin \frac{ 11\pi }{ 12 }=\sin(\frac{ 2\pi }{ 3 }+\frac{ \pi }{ 4 })=\sin \frac{ 2\pi }{ 3 }\cos \frac{ \pi }{ 4}+\cos \frac{ 2\pi }{ 3 }\sin \frac{ \pi }{ 4 }\]

Answer 11

Ok, but how can I get it to the root of a root form?

Answer 12

it looks like you don't have to do that, and if you use the unit circle to find those value it will give you the answer

Answer 13

So, I'm still a little confused what to do with sin2π3cosπ4+cos2π3sinπ4

Answer 14

what's sin (2pi/3)? Use your unit circle?

Answer 15

Sq. Rt3/2?

Answer 16

right. Now do cos π/4

Answer 17

Sqrt2/2

Answer 18

so far we have (√3)/2 * (√2)/2

Answer 19

Oh I get it.

Answer 20

great :). now do the other 2

Answer 21

Yep thank you!!!

Answer 22

you're welcome