Question

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..

Answer 1

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

Answer 2

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

Answer 3

oh quadrants

Answer 4

quadrant 2 is between pi/2 and pi

Answer 5

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

Answer 6

it will not be the cleanest value

Answer 7

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

Answer 8

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

Answer 9

applied to sin function

Answer 10

This whole question is just confusing me on top of that right now lol its asking for it to be in exact form

Answer 11

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

Answer 12

Without a calculator sadly...

Answer 13

hmm...

Answer 14

:3

Answer 15

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

Answer 16

uhh no i just doodled, its a highly inaccurate diagram

Answer 17

I don't even think he knows

Answer 18

Still need help on this one shorty? :)

Answer 19

Yes pleaseee!

Answer 20

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

Answer 21

Let's apply that before we do anything else

Answer 22

\[\large\rm \sin\left(\theta+\frac{\pi}{6}\right)=\sin \theta \cos \frac{\pi}{6}+\sin\frac{\pi}{6}\cos \theta\]Do you understand how I applied that formula? :)

Answer 23

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 :/

Answer 24

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

Answer 25

But how would the work look like?

Answer 26

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

Answer 27

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

Answer 28

The work is correct right?

Answer 29

\[\large\rm \sin\left(\theta+\frac{\pi}{6}\right)=\left(\sin \theta\right)\left(\cos \frac{\pi}{6}\right)+\left(\sin\frac{\pi}{6}\right)\left(\cos \theta\right)\]\[\large\rm \sin\left(\theta+\frac{\pi}{6}\right)=\left(\frac{3}{5}\right)\left(\frac{\sqrt3}{2}\right)+\left(\frac{1}{2}\right)\left(\frac{-4}{5}\right)\]

Answer 30

Plugging in the pieces :) ya looks right

Answer 31

But is there a way to check it?

Answer 32

Hmmm.

Answer 33

He is using the Sum and Difference formula.

Answer 34

\[\large\rm \sin(\theta)=\frac{3}{5}\qquad\to\qquad \sin^{-1}\frac{3}{5}=\theta\approx0.6435\]
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 :)

Answer 35

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

Answer 36

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