## anonymous 5 years ago use a double- angle identity to find the exact value sin22.5^ocos22.5^o

1. anonymous

why I am still at 19 fans, after spending the last 5 hours working my *** out?

2. anonymous

if you help me with this i will become a fan

3. anonymous

ok, one min

4. anonymous

the double angle identities are as follows: $\cos (A - B) = (\cos A)(\cos B) + (\sin A)(\sin B)$ $\cos (A + B) = (\cos A)\cos B - (\sin A)\sin B$ $\sin (A + B) = (\sin A)(\cos B) + (\cos A)(\sin B)$ $\sin (A - B) = (\sin A)(\cos B) - (\cos A)(\sin B)$ alright andy :) you can lead from here ^_^

5. anonymous

hmm, am I mixing it all up with the double angle identities? those are the sin and cos indentities , hmm, please correct me if I'm wrong ^_^

6. anonymous

double angle identities go like this, egzample: sin(2x)=2sinxcosx

7. nowhereman

That is just the above with setting A=B

8. anonymous

no the identities are sin2A=2sineAcosA cos2A-cos^2A-sin^2A =1-2sin^2A =2cosA-1

9. anonymous

or right lol , thank you, alright angoo, give it a try ^_^

10. anonymous

ok I am bad at this, I guess I must have skipped school the day this stuff was tought

11. anonymous

give it a try :)

12. anonymous

yeah same here

13. anonymous

nah, stary, you go ahead, I dont get this stuff yet

14. anonymous

15. anonymous

well, Google can give me examples, and explanations, and I can learn from them, but it would take too much time... so just go ahead and do it mimi

16. anonymous

this is my new signature btw: ▓▒░╔ᴧᴨᴅᴙiᴜs╖░▒▓

17. anonymous

LOL

18. anonymous

alright LoveL , let me get this clear : you want to find the answer of : sin(22.5)cos(22.5)? or do you want to find the exact angle for sin(22.5)=? or cos(22.5)=? ^_^ lol, it's filled with mystery, but I like it :)

19. nowhereman

I will show you, first of all: $\sin (22.5^\circ)\cos(22.5^\circ) = \sin(\frac{180^\circ}{8})\cos(\frac{180^\circ}{8}) = \sin(\frac{π}{8})\cos(\frac π 8)$

20. anonymous

21. anonymous

so, loveinglife, do you feel happy today? because I do, but I could become even more happy if you gift me a fan =D In that case, I will give you a fan too, so you become a lifesaver, and I become a superstar, a clear winwin =D

22. anonymous

LOL, and you're still on it

23. anonymous

@BecomeMyFan im your fan now. thank you for trying

24. nowhereman

Then $\sin(\frac π 8)\cos(\frac π 8) = \frac 1 2 \cdot \left(2\sin(\frac π 8)\cos(\frac π 8)\right)$ Thus by applying that double arc formula on the inner part (in reverse direction if you want) you get $=\frac 1 2 \sin(2\frac π 8) = \frac 1 2\sin(\frac π 4) = \frac 1 4 \sqrt 2$

25. anonymous

Oh my god your awesome. thank you soo much you just saved my trig grade

26. nowhereman

You're welcome :-D

27. anonymous

love, are you in highschool?

28. anonymous

or in college

29. anonymous

?

30. anonymous

because if you are doing this stuff in high school, I must have skipped ALOT of it

31. anonymous

im saddly in college and i thought i was good in math till i got here

32. anonymous

:)

33. anonymous

why am I still a mear star?

34. anonymous

I wanna be a superstar

35. anonymous

it was supposed to rhyme

36. anonymous

=D

37. anonymous

sorry cant help you there but im done, but i will probably be back at some point

38. anonymous

it is part of a poem I am writting about OpenStudy

39. anonymous

=)

40. anonymous

you write poems?