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

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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

Mathematics
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\[\sin (\theta + \alpha) = \sin \theta \cos \alpha + \sin \alpha \cos \theta\]
therefore: \[\sin (\theta + \frac{ \pi }{ 6}) = \sin \theta \cos \frac{ \pi }{ 6 } + \sin \frac{ \pi }{ 6 } \cos \theta\]
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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|dw:1436542535457:dw| also note: \[\pi/6 = 180/6 = 30\]
@butterflydreamer I am working it out but I don't think its right tho
you have the right idea :) BUT note that \[\sin \theta = \frac{ 3 }{ 5 } \]
hang on give me a minute :)
@butterflydreamer I thought I had finally got it :D but then I still got the wrong answer -___-
Does it have to do with it being in Quad 2?
did you change sin theta = 1/2 to sin theta = 3/5 ?
yeah I did that :/
oh ALSO! we have to work out what cos theta equals to
so we did change it after
hmm what is the final answer? i want to check that i have it right before showing you the way i did it :)
do you have any idea about correct answer?
The answer i got is .0866025
you can find the value of cos theta by formula \[\cos ^{2}=1- \sin ^{2}\theta\]
and then simply put all the value in the equation
alright, well i've written up my working out. Not 100% sure this is correct but i'll upload it in a bit :)
@butterflydreamer theres a way to check it if its right so we'll see :D
It didnt upload for some reasn lol
waiiit give me a min xD
-4/5 not - 3/5
i know xD my bad http://prntscr.com/7r45nc
:)
do you understand what i did? @shortyyshayy ^_^
@butterflydreamer yeah trying it out right now to see if its right so fingers crossed
okey dokeyy *crosses fingers*
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
-.-... sigh. What is the answer "meant" to be then?
.901 when you plug it back it in the original equation of sin theta + pi over 6
when you plug 3/5 in for theta I mean
hmm.. i don't think you can do that because: |dw:1436544628958:dw|
so it is the correct answer :) but you would plug in \[\theta = \sin^{-1} (3/5) \] into the equation :)
Wait whats the correct answer then? MY heads going to explode XD
So checking the work like sin (3/5 + pi/6) is wrong?
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 \[\sin( \theta + \frac{ \pi }{ 6 }) = \frac{ 3 \sqrt 3 - 4 }{ 10 }\]
can you upload your work again please lol? just so I can use it as a reference lol?
sureee,
Our professor showed us how to check our answer but your method and my method either of them don't work out XD
http://prntscr.com/7r4e4w
i know right xD I know that's the answer.. but idk why i can't check it -.-...
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?
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
What was the drawing you were showing me above with the inverse?
it was me thinking i was onto something (only to fall short) xD don't worry about it because it doesn't work anyway -.-
anyways, i'm heading off to bed now (it's 2:27am here) . I HOPE that my working out was correct
lmaoo no way? Ohmygod thanks so much for helping me out!! haha night!!

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