anonymous
  • anonymous
Find an exact value. sine of negative eleven pi divided by twelve.
Mathematics
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anonymous
  • anonymous
Find an exact value. sine of negative eleven pi divided by twelve.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
welshfella
  • welshfella
sien -11 p / 12 now we can find the value of sine of -11pi/ 6 which is half of -11pi/12
welshfella
  • welshfella
|dw:1438258865764:dw|

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welshfella
  • welshfella
- sin 11pi/6 = sin pi/6 = 1/2
arindameducationusc
  • arindameducationusc
sin(11pi+pi/6)=1/2 so, sin(-11/12)=....
welshfella
  • welshfella
now to find sin -11pi/12 we using the half angle formula sin -11pi/12 = sin pi/6 ------------ 1 + cos pi/6
welshfella
  • welshfella
i'll just check that is ok - - im relying on my memory here
anonymous
  • anonymous
wait I'm still a little lost
welshfella
  • welshfella
oops sorry thats the half-angle tan formula
welshfella
  • welshfella
i mad a mistake there where are you lost?
anonymous
  • anonymous
well I wouldn't say lost, I was here for this lecture and I don't know where these numbers are coming from.
anonymous
  • anonymous
wasn't
arindameducationusc
  • arindameducationusc
hey.... sin(pi/12-pi) =sin pi/12*cos pi - sin pi * cos pi/2 =.25882(-1) -0 =-.25882
arindameducationusc
  • arindameducationusc
using Trignometry identity.... sin(a-b)=sinacosb - cosasinb
arindameducationusc
  • arindameducationusc
This should help....
arindameducationusc
  • arindameducationusc
and above you are wondering how did .25882 come, its the value of sin(pi/12)
anonymous
  • anonymous
Ok, ya I'll get back to it later I have class soon. Thanks guys! :)
arindameducationusc
  • arindameducationusc
now how did I bring sin(pi/12) value....
arindameducationusc
  • arindameducationusc
okay... will wait.....
anonymous
  • anonymous
Really I have to go but I'll be back on in 2-3 hours.
anonymous
  • anonymous
That cool? :)
welshfella
  • welshfella
@arindameducationusc - you have a correct answer using the calculator but she wants an exact answer derived form known values like pi/6 = 1/2 and a trig identity. I got the wrong identity.
anonymous
  • anonymous
Ok.
Jhannybean
  • Jhannybean
Remember your formulas. \(\sin(\alpha + \beta) = \sin(\alpha)\cdot \cos(\beta) + \cos(\alpha)\cdot \sin(\beta)\)
anonymous
  • anonymous
Ok.
Jhannybean
  • Jhannybean
So let's say... \(-\dfrac{11\pi}{12} = -\dfrac{2\pi}{3}-\dfrac{\pi}{4}\) Can you go from there?
Jhannybean
  • Jhannybean
It's all a little plug and chug from there.
welshfella
  • welshfella
yes thats a good way to do it
welshfella
  • welshfella
another way would be to use the identity sin^2 (-11p/12) = [ 1 - cos (-11pi/6) ]/ 2
Jhannybean
  • Jhannybean
Oh that's another way, didn't think of that one too quickly.
Jhannybean
  • Jhannybean
You have a good day @welshfella , See ya around :)
welshfella
  • welshfella
yea theres so many trig identities - I used to know them all when i was younger Memories a bit hazy now!!1
welshfella
  • welshfella
yea you too
arindameducationusc
  • arindameducationusc
@welshfella sin15 can be derived easily....
arindameducationusc
  • arindameducationusc
Sin(45-30)... Using identity @welshfella I would have written it but she went offline
welshfella
  • welshfella
yes
welshfella
  • welshfella
thats another way too
arindameducationusc
  • arindameducationusc
@welshfella Thumbs up :)
anonymous
  • anonymous
u should close this now lol @clairvoyant1

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