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

- anonymous

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- butterflydreamer

\[\sin (\theta + \alpha) = \sin \theta \cos \alpha + \sin \alpha \cos \theta\]

- butterflydreamer

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

- 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) :)

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## More answers

- butterflydreamer

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

- anonymous

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

##### 1 Attachment

- butterflydreamer

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

- butterflydreamer

hang on give me a minute :)

- anonymous

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

- anonymous

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

- butterflydreamer

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

- anonymous

yeah I did that :/

- butterflydreamer

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

- anonymous

##### 1 Attachment

- anonymous

so we did change it after

- butterflydreamer

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

- anonymous

do you have any idea about correct answer?

- anonymous

The answer i got is .0866025

- anonymous

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

- anonymous

and then simply put all the value in the equation

- butterflydreamer

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

- anonymous

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

- anonymous

It didnt upload for some reasn lol

- butterflydreamer

waiiit give me a min xD

- xapproachesinfinity

-4/5 not - 3/5

- butterflydreamer

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

- xapproachesinfinity

:)

- butterflydreamer

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

- anonymous

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

- butterflydreamer

okey dokeyy *crosses fingers*

- 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

- butterflydreamer

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

- anonymous

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

- anonymous

when you plug 3/5 in for theta I mean

- butterflydreamer

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

- butterflydreamer

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

- anonymous

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

- anonymous

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

- 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
\[\sin( \theta + \frac{ \pi }{ 6 }) = \frac{ 3 \sqrt 3 - 4 }{ 10 }\]

- anonymous

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

- butterflydreamer

sureee,

- anonymous

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

- butterflydreamer

http://prntscr.com/7r4e4w

- butterflydreamer

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

- 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?

- 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

- anonymous

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

- 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 -.-

- butterflydreamer

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

- anonymous

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

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