anonymous
  • anonymous
If sin theta=3/5 and theta is in quadrant 2 determine in exact form sin theta+pi over 6
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Loser66
  • 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
  • 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
  • Loser66
show your work, please

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anonymous
  • anonymous
Alright the end work I got 3sqrt3 over 10 + 2/5 but it doesn't come out correct -___-
Loser66
  • 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
  • anonymous
But I still keep getting .919... answer ohmygod this is so frustarting lol @Loser66
anonymous
  • anonymous
And when you go to check the answer it is suppose to be .90166
freckles
  • freckles
http://www.wolframalpha.com/input/?i=%283%2F5%29+%28sqrt%283%29%2F2%29+%2B+%281%2F2%29+%284%2F5%29+
freckles
  • freckles
that is what it says when I punch in what loser has above
freckles
  • freckles
and 0.9196 is also what I'm getting
freckles
  • freckles
i think you are right @shortyyshayy
freckles
  • freckles
and they have an error
anonymous
  • anonymous
@freckles Idk this is coming out weird cuz when checking it I am like a .1 off lol
freckles
  • freckles
just to be sure you are asked to evaluate \[\sin(\theta+\frac{\pi}{6})\]
freckles
  • freckles
well the other thing is it says it wants the EXACT form not an approximation
freckles
  • freckles
exact form would be \[\frac{2}{5}+\frac{3 \sqrt{3}}{10}\]
freckles
  • freckles
not .9196
freckles
  • freckles
which is just an approximation
Loser66
  • Loser66
https://www.google.com/?gws_rd=ssl#q=online+calculator
freckles
  • freckles
omg I'm so dumb
freckles
  • freckles
I didn't see it said in quadrant 2
freckles
  • freckles
cos is negative there
freckles
  • freckles
\[\frac{3}{5} \frac{\sqrt{3}}{2}+\frac{-4}{5}\frac{1}{2}\]
freckles
  • freckles
which actually gives us .1196 so that still doesn't give us the answer you want
Loser66
  • Loser66
yes!!! @freckles
anonymous
  • anonymous
where did you get -4/5 from tho??
freckles
  • freckles
it says theta is in quadrant 2
freckles
  • freckles
cos is negative there and sin is positive there
freckles
  • freckles
sin(theta)=3/5 cos(theta) can be 4/5 or -4/5 depending on where theta is
freckles
  • freckles
and since cos is negative then cos(theta)=-4/5
freckles
  • 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
  • freckles
now deciding whether to use 4/5 or -4/5 entirely depends on where theta is
freckles
  • freckles
|dw:1436467227803:dw|
anonymous
  • anonymous
@freckles ohhh alright i think this is making more sense now! haha thanks so much!!!
freckles
  • freckles
|dw:1436467279746:dw|
freckles
  • freckles
hey so why are you looking for an approximation anyways?
freckles
  • freckles
you problem wants exact form
anonymous
  • anonymous
I thought thats what it wanted in the first place lol
freckles
  • 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
  • freckles
like the .1196 is an approximation to that exact form
freckles
  • freckles
.1196 is not exactly 3sqrt(3)/10-2/5 that is the funny thing about irrational numbers

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