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..

- anonymous

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- anonymous

I dont understand what you are asking, what do you mean by 'quad 2'.

- anonymous

14mdaz, you have different quadrants when dealing with the unit circle and that is what he/she is referring to

- anonymous

oh quadrants

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## More answers

- anonymous

quadrant 2 is between pi/2 and pi

- anonymous

What I don't get is what he / she is wanting from the exact form of sin (theta+ pi/6) is

- anonymous

it will not be the cleanest value

- anonymous

Is he wanting to add sin theta=3/5 + pi/6???

- anonymous

no he wants theta plus pi/6 all in rads im guessing

- anonymous

applied to sin function

- 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

Are you allowed to use a calculator or do you need to find \( \sin \theta = 3/5 \) without a calculator?

- anonymous

Without a calculator sadly...

- anonymous

hmm...

- anonymous

|dw:1436649831637:dw|

- anonymous

:3

- anonymous

I think 14mdaz is explaining so I am going to step back

- anonymous

uhh no i just doodled, its a highly inaccurate diagram

- anonymous

I don't even think he knows

- zepdrix

Still need help on this one shorty? :)

- anonymous

Yes pleaseee!

- zepdrix

You need to apply your Angle Sum Formula:\[\large\rm \sin(\alpha+\beta)=\sin \alpha \cos \beta+\sin \beta \cos \alpha\]

- zepdrix

Let's apply that before we do anything else

- 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

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

Oooo yes good job!
That looks correct!! :)

- anonymous

But how would the work look like?

- anonymous

But when I go to check my answer something comes out differently.

- anonymous

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

- anonymous

The work is correct right?

- 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

Plugging in the pieces :) ya looks right

- anonymous

But is there a way to check it?

- zepdrix

Hmmm.

- anonymous

He is using the Sum and Difference formula.

- 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

You can easily check with a calculator. Just plugin the values

- anonymous

Oh alright cuz my professor was all like you can check your work which is why I was asking

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