## anonymous one year ago 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..

1. anonymous

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

2. anonymous

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

3. anonymous

4. anonymous

quadrant 2 is between pi/2 and pi

5. anonymous

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

6. anonymous

it will not be the cleanest value

7. anonymous

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

8. anonymous

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

9. anonymous

applied to sin function

10. anonymous

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

11. anonymous

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

12. anonymous

13. anonymous

hmm...

14. anonymous

|dw:1436649831637:dw|

15. anonymous

:3

16. anonymous

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

17. anonymous

uhh no i just doodled, its a highly inaccurate diagram

18. anonymous

I don't even think he knows

19. zepdrix

Still need help on this one shorty? :)

20. anonymous

21. zepdrix

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

22. zepdrix

Let's apply that before we do anything else

23. 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? :)

24. 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 :/

25. zepdrix

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

26. anonymous

But how would the work look like?

27. anonymous

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

28. anonymous

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

29. anonymous

The work is correct right?

30. 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)$

31. zepdrix

Plugging in the pieces :) ya looks right

32. anonymous

But is there a way to check it?

33. zepdrix

Hmmm.

34. anonymous

He is using the Sum and Difference formula.

35. 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 :)

36. anonymous

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

37. anonymous

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