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## anonymous one year ago 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

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1. anonymous

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

2. anonymous

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

3. anonymous

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.

4. anonymous

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

5. anonymous

actually hold up

6. anonymous

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

7. anonymous

Yes, I think so.

8. anonymous

what did you get when you did it?

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous

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

15. anonymous

Sq. Rt3/2?

16. anonymous

right. Now do cos π/4

17. anonymous

Sqrt2/2

18. anonymous

so far we have (√3)/2 * (√2)/2

19. anonymous

Oh I get it.

20. anonymous

great :). now do the other 2

21. anonymous

Yep thank you!!!

22. anonymous

you're welcome

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