## anonymous one year ago Find an exact value. sine of negative eleven pi divided by twelve.

1. anonymous

@welshfella

2. welshfella

sien -11 p / 12 now we can find the value of sine of -11pi/ 6 which is half of -11pi/12

3. welshfella

|dw:1438258865764:dw|

4. welshfella

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

5. arindameducationusc

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

6. welshfella

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

7. welshfella

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

8. anonymous

wait I'm still a little lost

9. welshfella

oops sorry thats the half-angle tan formula

10. welshfella

i mad a mistake there where are you lost?

11. anonymous

well I wouldn't say lost, I was here for this lecture and I don't know where these numbers are coming from.

12. anonymous

wasn't

13. arindameducationusc

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

14. arindameducationusc

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

15. arindameducationusc

This should help....

16. arindameducationusc

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

17. anonymous

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

18. arindameducationusc

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

19. arindameducationusc

okay... will wait.....

20. anonymous

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

21. anonymous

That cool? :)

22. 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.

23. anonymous

Ok.

24. anonymous

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

25. anonymous

Ok.

26. anonymous

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

27. anonymous

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

28. welshfella

yes thats a good way to do it

29. welshfella

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

30. anonymous

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

31. anonymous

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

32. welshfella

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

33. welshfella

yea you too

34. arindameducationusc

@welshfella sin15 can be derived easily....

35. arindameducationusc

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

36. welshfella

yes

37. welshfella

thats another way too

38. arindameducationusc

@welshfella Thumbs up :)

39. anonymous

u should close this now lol @clairvoyant1