## anonymous one year ago If sin theta=3/5 and theta is in quadrant 2 determine in exact form sin theta+pi over 6

1. 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|

2. 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

3. Loser66

4. anonymous

Alright the end work I got 3sqrt3 over 10 + 2/5 but it doesn't come out correct -___-

5. 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

6. anonymous

But I still keep getting .919... answer ohmygod this is so frustarting lol @Loser66

7. anonymous

And when you go to check the answer it is suppose to be .90166

8. freckles
9. freckles

that is what it says when I punch in what loser has above

10. freckles

and 0.9196 is also what I'm getting

11. freckles

i think you are right @shortyyshayy

12. freckles

and they have an error

13. anonymous

@freckles Idk this is coming out weird cuz when checking it I am like a .1 off lol

14. freckles

just to be sure you are asked to evaluate $\sin(\theta+\frac{\pi}{6})$

15. freckles

well the other thing is it says it wants the EXACT form not an approximation

16. freckles

exact form would be $\frac{2}{5}+\frac{3 \sqrt{3}}{10}$

17. freckles

not .9196

18. freckles

which is just an approximation

19. Loser66
20. freckles

omg I'm so dumb

21. freckles

I didn't see it said in quadrant 2

22. freckles

cos is negative there

23. freckles

$\frac{3}{5} \frac{\sqrt{3}}{2}+\frac{-4}{5}\frac{1}{2}$

24. freckles

which actually gives us .1196 so that still doesn't give us the answer you want

25. Loser66

yes!!! @freckles

26. anonymous

where did you get -4/5 from tho??

27. freckles

it says theta is in quadrant 2

28. freckles

cos is negative there and sin is positive there

29. freckles

sin(theta)=3/5 cos(theta) can be 4/5 or -4/5 depending on where theta is

30. freckles

and since cos is negative then cos(theta)=-4/5

31. freckles

here is another way to look at it we are given sin(theta)=3/5 $\cos^2(\theta)+\sin^2(\theta)=1 \\ \cos^2(\theta)+(\frac{3}{5})^2=1 \\ \cos^2(\theta)+\frac{9}{25}=1 \\ \cos^2(\theta)=1-\frac{9}{25} \\ \cos^2(\theta)=\frac{25}{25}-\frac{9}{25} \\ \cos^2(\theta)=\frac{16}{25} \\ \cos(\theta)=\pm \sqrt{\frac{16}{25}} \\ \cos(\theta)=\pm \frac{4}{5}$

32. freckles

now deciding whether to use 4/5 or -4/5 entirely depends on where theta is

33. freckles

|dw:1436467227803:dw|

34. anonymous

@freckles ohhh alright i think this is making more sense now! haha thanks so much!!!

35. freckles

|dw:1436467279746:dw|

36. freckles

hey so why are you looking for an approximation anyways?

37. freckles

you problem wants exact form

38. anonymous

I thought thats what it wanted in the first place lol

39. 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

40. freckles

like the .1196 is an approximation to that exact form

41. freckles

.1196 is not exactly 3sqrt(3)/10-2/5 that is the funny thing about irrational numbers