## DLS 2 years ago find theta!

1. DLS

$\LARGE \sqrt{3}\sin \theta-\cos \theta=2$

2. hartnn

$$\LARGE (\sqrt{3}/2)\sin \theta-(1/2)\cos \theta=2/2$$

3. DLS

you're the man!

4. hartnn

now write cos a = \sqrt 3/2 ,sin a =1/2

5. hartnn

where a=...?

6. DLS

60

7. DLS

pi/3

8. hartnn

no.

9. DLS

oh sorry!!

10. DLS

pi/6

11. hartnn

sin ... = 1/2 ?

12. hartnn

yes.

13. UsukiDoll

30 degrees

14. hartnn

what is $$cos 30sin \theta-sin30 cos \theta=..?$$

15. DLS

i messed up u,u

16. DLS

sin(A-B)

17. UsukiDoll

|dw:1356774577698:dw|

18. hartnn

sin [$$\theta$$-30] = 1 = sin 90

19. hartnn

got that ^ ?

20. DLS

i didnt get that diag! but yes what u said

21. DLS

okay got the diag too

22. hartnn

so, theta =... ?

23. UsukiDoll

I was drawing the triangle with its values 0_0

24. DLS

pi/2 right?what else :/

25. UsukiDoll

|dw:1356774667353:dw|

26. hartnn

that means , you didn't get this... sin [θ-30] = 1 = sin 90

27. DLS

im getting embarassed with so many people viewing this ques lloll

28. LogicalApple

We are all curious!

29. hba

Interesting question :P

30. hartnn

dls, write the step till how much u understood totally.

31. DLS

okay

32. DLS

why did we interchange the values cos a = \sqrt 3/2 ,sin a =1/2? we had sin with sqrt 3/2 and cos with 1/2

33. hartnn

when did we have sin with sqrt 3/2 ?? and you can take that also, then u have to use a different formula.

34. DLS

ur first post O_O

35. hartnn

$$\LARGE (\sqrt{3}/2)\sin \theta-(1/2)\cos \theta=2/2$$ $$\LARGE \cos 30\sin \theta-\sin 30\cos \theta=1$$ $$\sin(\theta-30)=sin 90 \\ \theta =...?$$

36. DLS

120?

37. hartnn

yes, u got it ?

38. DLS

yes..much better when u wrote that together !! and we had less people lol

39. DLS

we have only ONE possible value?

40. DLS

okay thats obv..thanks! and thanks to the spectators >>

41. hartnn

u want general expression ?

42. DLS

sure

43. DLS

but thats not reqd.i just wanted to know the possible values of theta from 0 to 2pi

44. hartnn

then only 120

45. DLS

yes..thats it!thanks!