If sin theta=3/5 and theta is in quadrant 2 determine in exact form sin theta+pi over 6

- anonymous

If sin theta=3/5 and theta is in quadrant 2 determine in exact form sin theta+pi over 6

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- Loser66

We have formula sin(a+b) = sin a *cos b + sin b *cos a
your a = theta
your b= pi/6
find cos theta, then plug all into it.
|dw:1436465382393:dw|

- anonymous

@Loser66 So I did all that and got the answer .9196 but I am off by a point when I check if it is right tho

- Loser66

show your work, please

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## More answers

- anonymous

Alright the end work I got 3sqrt3 over 10 + 2/5 but it doesn't come out correct -___-

- Loser66

cos (theta) = 4/5
hence sin (theta + pi/6) = sin (theta) cos (pi/6) + sin (pi/6) cos (theta)
= (3/5) (sqrt 3/2) + (1/2) (4/5) = 0.573

- anonymous

But I still keep getting .919... answer ohmygod this is so frustarting lol @Loser66

- anonymous

And when you go to check the answer it is suppose to be .90166

- freckles

http://www.wolframalpha.com/input/?i=%283%2F5%29+%28sqrt%283%29%2F2%29+%2B+%281%2F2%29+%284%2F5%29+

- freckles

that is what it says when I punch in what loser has above

- freckles

and 0.9196 is also what I'm getting

- freckles

i think you are right @shortyyshayy

- freckles

and they have an error

- anonymous

@freckles Idk this is coming out weird cuz when checking it I am like a .1 off lol

- freckles

just to be sure you are asked to evaluate
\[\sin(\theta+\frac{\pi}{6})\]

- freckles

well the other thing is it says it wants the EXACT form
not an approximation

- freckles

exact form would be
\[\frac{2}{5}+\frac{3 \sqrt{3}}{10}\]

- freckles

not .9196

- freckles

which is just an approximation

- Loser66

https://www.google.com/?gws_rd=ssl#q=online+calculator

- freckles

omg I'm so dumb

- freckles

I didn't see it said in quadrant 2

- freckles

cos is negative there

- freckles

\[\frac{3}{5} \frac{\sqrt{3}}{2}+\frac{-4}{5}\frac{1}{2}\]

- freckles

which actually gives us .1196
so that still doesn't give us the answer you want

- Loser66

yes!!! @freckles

- anonymous

where did you get -4/5 from tho??

- freckles

it says theta is in quadrant 2

- freckles

cos is negative there
and
sin is positive there

- freckles

sin(theta)=3/5
cos(theta) can be 4/5 or -4/5 depending on where theta is

- freckles

and since cos is negative then cos(theta)=-4/5

- freckles

here is another way to look at it
we are given sin(theta)=3/5
\[\cos^2(\theta)+\sin^2(\theta)=1 \\ \cos^2(\theta)+(\frac{3}{5})^2=1 \\ \cos^2(\theta)+\frac{9}{25}=1 \\ \cos^2(\theta)=1-\frac{9}{25} \\ \cos^2(\theta)=\frac{25}{25}-\frac{9}{25} \\ \cos^2(\theta)=\frac{16}{25} \\ \cos(\theta)=\pm \sqrt{\frac{16}{25}} \\ \cos(\theta)=\pm \frac{4}{5}\]

- freckles

now deciding whether to use 4/5 or -4/5 entirely depends on where theta is

- freckles

|dw:1436467227803:dw|

- anonymous

@freckles ohhh alright i think this is making more sense now! haha thanks so much!!!

- freckles

|dw:1436467279746:dw|

- freckles

hey so why are you looking for an approximation anyways?

- freckles

you problem wants exact form

- anonymous

I thought thats what it wanted in the first place lol

- freckles

\[\frac{3}{5} \frac{\sqrt{3}}{2}+\frac{-4}{5}\frac{1}{2} \\ \frac{3 \sqrt{3}}{10}-\frac{2}{5}\]
this is exact form

- freckles

like the .1196 is an approximation to that exact form

- freckles

.1196 is not exactly 3sqrt(3)/10-2/5
that is the funny thing about irrational numbers

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