anonymous
  • anonymous
If sin theta=3/5 and theta is in quad 2 the exact form of sin (theta+ pi/6) is .....? literally have not figured out this question at all..
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I dont understand what you are asking, what do you mean by 'quad 2'.
anonymous
  • anonymous
14mdaz, you have different quadrants when dealing with the unit circle and that is what he/she is referring to
anonymous
  • anonymous
oh quadrants

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anonymous
  • anonymous
quadrant 2 is between pi/2 and pi
anonymous
  • anonymous
What I don't get is what he / she is wanting from the exact form of sin (theta+ pi/6) is
anonymous
  • anonymous
it will not be the cleanest value
anonymous
  • anonymous
Is he wanting to add sin theta=3/5 + pi/6???
anonymous
  • anonymous
no he wants theta plus pi/6 all in rads im guessing
anonymous
  • anonymous
applied to sin function
anonymous
  • anonymous
This whole question is just confusing me on top of that right now lol its asking for it to be in exact form
anonymous
  • anonymous
Are you allowed to use a calculator or do you need to find \( \sin \theta = 3/5 \) without a calculator?
anonymous
  • anonymous
Without a calculator sadly...
anonymous
  • anonymous
hmm...
anonymous
  • anonymous
|dw:1436649831637:dw|
anonymous
  • anonymous
:3
anonymous
  • anonymous
I think 14mdaz is explaining so I am going to step back
anonymous
  • anonymous
uhh no i just doodled, its a highly inaccurate diagram
anonymous
  • anonymous
I don't even think he knows
zepdrix
  • zepdrix
Still need help on this one shorty? :)
anonymous
  • anonymous
Yes pleaseee!
zepdrix
  • zepdrix
You need to apply your Angle Sum Formula:\[\large\rm \sin(\alpha+\beta)=\sin \alpha \cos \beta+\sin \beta \cos \alpha\]
zepdrix
  • zepdrix
Let's apply that before we do anything else
zepdrix
  • zepdrix
\[\large\rm \sin\left(\theta+\frac{\pi}{6}\right)=\sin \theta \cos \frac{\pi}{6}+\sin\frac{\pi}{6}\cos \theta\]Do you understand how I applied that formula? :)
anonymous
  • anonymous
Yeah I think I have done it that way and got the answer [3*sqrt(3) - 4]/10 but I don't think its right :/
zepdrix
  • zepdrix
Oooo yes good job! That looks correct!! :)
anonymous
  • anonymous
But how would the work look like?
anonymous
  • anonymous
But when I go to check my answer something comes out differently.
anonymous
  • anonymous
sin(theta)cos(pi/6) + cos(theta)sin(pi/6) = (3/5)(sqrt(3)/2) - (4/5)(1/2)
anonymous
  • anonymous
The work is correct right?
zepdrix
  • zepdrix
\[\large\rm \sin\left(\theta+\frac{\pi}{6}\right)=\left(\sin \theta\right)\left(\cos \frac{\pi}{6}\right)+\left(\sin\frac{\pi}{6}\right)\left(\cos \theta\right)\]\[\large\rm \sin\left(\theta+\frac{\pi}{6}\right)=\left(\frac{3}{5}\right)\left(\frac{\sqrt3}{2}\right)+\left(\frac{1}{2}\right)\left(\frac{-4}{5}\right)\]
zepdrix
  • zepdrix
Plugging in the pieces :) ya looks right
anonymous
  • anonymous
But is there a way to check it?
zepdrix
  • zepdrix
Hmmm.
anonymous
  • anonymous
He is using the Sum and Difference formula.
zepdrix
  • zepdrix
\[\large\rm \sin(\theta)=\frac{3}{5}\qquad\to\qquad \sin^{-1}\frac{3}{5}=\theta\approx0.6435\] So then the sine of that angle theta... plus pi/6 should approximately give us (3sqrt3-4)/10, whatever decimal that works out to. Kind of a tough problem to check your work on :)
anonymous
  • anonymous
You can easily check with a calculator. Just plugin the values
anonymous
  • anonymous
Oh alright cuz my professor was all like you can check your work which is why I was asking

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