anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • 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
anonymous
  • anonymous
Ok, but how can I get the answers like the ones I was given?
anonymous
  • 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.

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More answers

anonymous
  • 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
anonymous
  • anonymous
actually hold up
anonymous
  • anonymous
ok so you used the \(\sin(a + b) = \sin a \cos b + \cos a \sin b \) identity?
anonymous
  • anonymous
Yes, I think so.
anonymous
  • anonymous
what did you get when you did it?
anonymous
  • anonymous
Well, I only have right now, 2pi/3 + pi/4
anonymous
  • anonymous
you have to substitute the values you got into the equation and evaluate it\[\sin \frac{ 11\pi }{ 12 }=\sin(\frac{ 2\pi }{ 3 }+\frac{ \pi }{ 4 })=\sin \frac{ 2\pi }{ 3 }\cos \frac{ \pi }{ 4}+\cos \frac{ 2\pi }{ 3 }\sin \frac{ \pi }{ 4 }\]
anonymous
  • anonymous
Ok, but how can I get it to the root of a root form?
anonymous
  • 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
anonymous
  • anonymous
So, I'm still a little confused what to do with sin2π3cosπ4+cos2π3sinπ4
anonymous
  • anonymous
what's sin (2pi/3)? Use your unit circle?
anonymous
  • anonymous
Sq. Rt3/2?
anonymous
  • anonymous
right. Now do cos π/4
anonymous
  • anonymous
Sqrt2/2
anonymous
  • anonymous
so far we have (√3)/2 * (√2)/2
anonymous
  • anonymous
Oh I get it.
anonymous
  • anonymous
great :). now do the other 2
anonymous
  • anonymous
Yep thank you!!!
anonymous
  • anonymous
you're welcome

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