Find an exact value.
sine of negative eleven pi divided by twelve.

- anonymous

Find an exact value.
sine of negative eleven pi divided by twelve.

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- 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

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## More answers

- welshfella

- sin 11pi/6 = sin pi/6 = 1/2

- arindameducationusc

sin(11pi+pi/6)=1/2 so, sin(-11/12)=....

- welshfella

now to find sin -11pi/12
we using the half angle formula
sin -11pi/12 = sin pi/6
------------
1 + cos pi/6

- welshfella

i'll just check that is ok - - im relying on my memory here

- anonymous

wait I'm still a little lost

- welshfella

oops sorry thats the half-angle tan formula

- welshfella

i mad a mistake there
where are you lost?

- 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

wasn't

- arindameducationusc

hey....
sin(pi/12-pi)
=sin pi/12*cos pi - sin pi * cos pi/2
=.25882(-1) -0
=-.25882

- arindameducationusc

using Trignometry identity.... sin(a-b)=sinacosb - cosasinb

- arindameducationusc

This should help....

- arindameducationusc

and above you are wondering how did .25882 come, its the value of sin(pi/12)

- anonymous

Ok, ya I'll get back to it later I have class soon. Thanks guys! :)

- arindameducationusc

now how did I bring sin(pi/12) value....

- arindameducationusc

okay... will wait.....

- anonymous

Really I have to go but I'll be back on in 2-3 hours.

- anonymous

That cool? :)

- 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

Ok.

- Jhannybean

Remember your formulas. \(\sin(\alpha + \beta) = \sin(\alpha)\cdot \cos(\beta) + \cos(\alpha)\cdot \sin(\beta)\)

- anonymous

Ok.

- Jhannybean

So let's say... \(-\dfrac{11\pi}{12} = -\dfrac{2\pi}{3}-\dfrac{\pi}{4}\)
Can you go from there?

- Jhannybean

It's all a little plug and chug from there.

- welshfella

yes thats a good way to do it

- welshfella

another way would be to use the identity
sin^2 (-11p/12) = [ 1 - cos (-11pi/6) ]/ 2

- Jhannybean

Oh that's another way, didn't think of that one too quickly.

- Jhannybean

You have a good day @welshfella , See ya around :)

- welshfella

yea theres so many trig identities - I used to know them all when i was younger Memories a bit hazy now!!1

- welshfella

yea you too

- arindameducationusc

@welshfella sin15 can be derived easily....

- arindameducationusc

Sin(45-30)...
Using identity @welshfella
I would have written it but she went offline

- welshfella

yes

- welshfella

thats another way too

- arindameducationusc

@welshfella Thumbs up :)

- anonymous

u should close this now lol @clairvoyant1

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