## anonymous one year ago if sin theta=3/5 and theta is in quad 2 the exact form of sin (theta+ pi/6) is ..... I had already asked this question but still don't understand it

1. butterflydreamer

$\sin (\theta + \alpha) = \sin \theta \cos \alpha + \sin \alpha \cos \theta$

2. butterflydreamer

therefore: $\sin (\theta + \frac{ \pi }{ 6}) = \sin \theta \cos \frac{ \pi }{ 6 } + \sin \frac{ \pi }{ 6 } \cos \theta$

3. butterflydreamer

and then you want to use your exact value table to help you out here since they want the final answer in exact form (this means including radicals) :)

4. butterflydreamer

|dw:1436542535457:dw| also note: $\pi/6 = 180/6 = 30$

5. anonymous

@butterflydreamer I am working it out but I don't think its right tho

6. butterflydreamer

you have the right idea :) BUT note that $\sin \theta = \frac{ 3 }{ 5 }$

7. butterflydreamer

hang on give me a minute :)

8. anonymous

@butterflydreamer I thought I had finally got it :D but then I still got the wrong answer -___-

9. anonymous

Does it have to do with it being in Quad 2?

10. butterflydreamer

did you change sin theta = 1/2 to sin theta = 3/5 ?

11. anonymous

yeah I did that :/

12. butterflydreamer

oh ALSO! we have to work out what cos theta equals to

13. anonymous

14. anonymous

so we did change it after

15. butterflydreamer

hmm what is the final answer? i want to check that i have it right before showing you the way i did it :)

16. anonymous

17. anonymous

The answer i got is .0866025

18. anonymous

you can find the value of cos theta by formula $\cos ^{2}=1- \sin ^{2}\theta$

19. anonymous

and then simply put all the value in the equation

20. butterflydreamer

alright, well i've written up my working out. Not 100% sure this is correct but i'll upload it in a bit :)

21. anonymous

@butterflydreamer theres a way to check it if its right so we'll see :D

22. anonymous

It didnt upload for some reasn lol

23. butterflydreamer

waiiit give me a min xD

24. xapproachesinfinity

-4/5 not - 3/5

25. butterflydreamer

i know xD my bad http://prntscr.com/7r45nc

26. xapproachesinfinity

:)

27. butterflydreamer

do you understand what i did? @shortyyshayy ^_^

28. anonymous

@butterflydreamer yeah trying it out right now to see if its right so fingers crossed

29. butterflydreamer

okey dokeyy *crosses fingers*

30. anonymous

I had the same problem yesterday with this and people tried to help me but no luck and I checked it and still not the correct answer ohmygod Im so annoyed now with this problem lol

31. butterflydreamer

-.-... sigh. What is the answer "meant" to be then?

32. anonymous

.901 when you plug it back it in the original equation of sin theta + pi over 6

33. anonymous

when you plug 3/5 in for theta I mean

34. butterflydreamer

hmm.. i don't think you can do that because: |dw:1436544628958:dw|

35. butterflydreamer

so it is the correct answer :) but you would plug in $\theta = \sin^{-1} (3/5)$ into the equation :)

36. anonymous

Wait whats the correct answer then? MY heads going to explode XD

37. anonymous

So checking the work like sin (3/5 + pi/6) is wrong?

38. butterflydreamer

xD wait... i'm getting confused now LOLLL. well it when i do that, i get a different answer? T_T... I'm pretty sure working out is correct $\sin( \theta + \frac{ \pi }{ 6 }) = \frac{ 3 \sqrt 3 - 4 }{ 10 }$

39. anonymous

can you upload your work again please lol? just so I can use it as a reference lol?

40. butterflydreamer

sureee,

41. anonymous

Our professor showed us how to check our answer but your method and my method either of them don't work out XD

42. butterflydreamer
43. butterflydreamer

i know right xD I know that's the answer.. but idk why i can't check it -.-...

44. anonymous

So are you sure it's correct then cuz I might just put your answer lol? Cuz maybe its the way were both checking it?

45. butterflydreamer

i think it's correct. I looked at the previous time you uploaded the question, and it's the same answer so xD that's a sign LOL

46. anonymous

What was the drawing you were showing me above with the inverse?

47. butterflydreamer

it was me thinking i was onto something (only to fall short) xD don't worry about it because it doesn't work anyway -.-

48. butterflydreamer

anyways, i'm heading off to bed now (it's 2:27am here) . I HOPE that my working out was correct

49. anonymous

lmaoo no way? Ohmygod thanks so much for helping me out!! haha night!!