## anonymous 3 years ago Solve sin2x + 4sin x + 3 = 0

1. anonymous

do u know how to solve this ?

2. anonymous

sin(2x) is more interesting :)

3. anonymous

Is it sin^2x + 4sinx + 3 = 0 ?

4. anonymous

|dw:1345778720492:dw| i dont know why latex is not working..

5. ash2326

@Lulu212 Is it $$\sin 2x \ or \ \sin^2 x$$?

6. anonymous

sin 2x

7. Mimi_x3

$sin2x + 4sinx + 3$

8. Mimi_x3

$sin2x = 2sinxcosx$ $2sinxcosx + 4sinx + 3 = 0$

9. Mimi_x3

have you tried that yet?

10. anonymous

hm...hm.... u need...to find the General soln of this....!

11. anonymous

@UnkleRhaukus @Hero @jim_thompson5910 @myininaya

12. anonymous

@Hero @hartnn

13. UnkleRhaukus

$\sin(2x) + 4\sin (x) + 3 = 0$ $2\sin(x)\cos(x) + 4\sin (x) + 3 = 0$ $2\sin (x)\left(\cos(x)+2\right)+3=0$ $2\sin (x)\left(\cos(x)+2\right)=-3$ $\cos(x)+2=\frac{-3}2\csc(x)$ i dont know

14. anonymous

15. Hero

I don't understand why @UnkleRhaukus can't finish it

16. anonymous

Can u Finish @Hero i am also stuck..there

17. anonymous

@jim_thompson5910

18. Mimi_x3

hmm http://www.wolframalpha.com/input/?i=sin2x+%2B+4sin+x+%2B+3+%3D+0 i dont think its possible..

19. anonymous

i think..tthere is mistake in question..))))

20. anonymous

@Lulu212 can u check ur question...))

21. Mimi_x3

I think it should be $$sin^2x + 4sinx +3 =0$$

22. Mimi_x3

then $$u=sinx$$ more reasonable

23. anonymous

then it is a quad eq

24. anonymous

we can find sinx

25. Hero

I'm inclined to agree with @Mimi_x3

26. anonymous

this question can be solved ............why u guys are worrying????????

27. anonymous

it cant be solved just endless ways of writing the equation

28. anonymous

what are we solving for? LOL. that equation needs to be written precisely in a way that we all can agree to what it is.

29. UnkleRhaukus

$\sin^2x+4\sin x+3=0$ $u^2-4u+3=0$ $u=\frac{-(-4)\pm\sqrt{(-4)^2-4\times(1)\times(3)}}{2(1)}$ $u=2\pm\frac{\sqrt{4}}{2}$$u=2\pm1$$u=1,3$ $(1)^2+4(1)+3=0,\qquad\qquad 3^2-4(3)+3=0$$8=0,\qquad\qquad\qquad 3^2-4(3)+3=0$$\text{false}\qquad\qquad\qquad 9-12+3=0$$\qquad\qquad\qquad\qquad0=0$$\qquad\qquad\qquad\text{true}$

30. anonymous

the equation toolbar in this thing sucks hairy ______. how do you write it so neatly like that?

31. UnkleRhaukus

so $$u=\sin(x)=3$$ $x=\arcsin (3)$ ... this question is very confusing $\text{\[u=\frac{-(-4)\pm\sqrt{(-4)^2-4\times(1)\times(3)}}{2(1)}$}\]

32. UnkleRhaukus

oh damn my solution is way off $\sin^2(\arcsin 3) + 4\sin (\arcsin 3) + 3 = 24≠0$

33. UnkleRhaukus

oh $$u^2+4u+3=0$$ NOT $$u^2-4u+3=0$$

34. anonymous

but this wasnt the problem that was stated lol

35. UnkleRhaukus

$u_{1,2}=-2\pm1=-3,-1$

36. UnkleRhaukus

$\sin x=u=-3,-1$ $x_{1,2}=\arcsin (-1),\quad \arcsin(-3)$ $x_1=-\frac \pi2\qquad, x_2=\text{some transcendental nonsense}$ hence$x=-\frac {\pi}2$ CHECKING $\sin^2x + 4\sin x + 3 = 0$ $\sin^2\left(-\frac\pi 2\right) + 4\sin \left(-\frac\pi 2\right) + 3 = 0$$1+4(-1)+3=0$$0=0$true hence $\large{x=-\frac {\pi}2}$is the solution to $\sin^2x + 4\sin x + 3 = 0$

37. UnkleRhaukus

ta-da

38. Hero

People who post questions need to learn how to use the equation editors to avoid such confusion.

39. anonymous

couldn't agree more @Hero

40. UnkleRhaukus

i think someone needs to write a program that can interpet questions and convert them to $$\LaTeX$$ automagically

41. anonymous

@lulu212 i am disappoint at this equation

42. Hero

I imagine that something like that would have to be interactive. It would have to be some kind of AI that would automatically ask the user something like: Did you mean $$\sin(2x)$$ or $$\sin^2(x)$$?

43. anonymous

beyond OS' capacity :P we can ask Wolfram though. That dude is probably the smartest programmer I've seen alive

44. Hero

That's because he was reincarnated Einstein

45. anonymous

hahaha... I think he was already born when Einstein was still alive

46. Hero

Well, Einstein's lost twin

47. anonymous

this question has like 40 responses all because of a typing error

48. Hero

We're still assuming that it is a typing error

49. anonymous

it is

50. Hero

There's no such thing as typing errors. Only human errors.

51. anonymous

the person who asked for help did not even say anything after the question was posted (TYPOGRAPHICAL ERROR)

52. UnkleRhaukus

can't we all be einsteins lost twin?

53. anonymous

I know that I can't... I have a roach's brain compare to his

54. anonymous

same difference hero lol

55. UnkleRhaukus

twins dont necessarily have the same charistics

56. anonymous

oh that's right... I'd be the opposite of his intellect then

57. UnkleRhaukus

* characteristic

58. Hero

In one of Einstein's lost journals, he wrote that his brain was removed as a kid. The person handling his brain accidentally dropped in brain in a toilet, but quietly removed it without telling anyone. Once the brain was placed back into Einstein's head, he felt different, like as if he had more 'powers' and 'ability'. We all know what that led to.

59. UnkleRhaukus

oh my.

60. anonymous

where's David Hume?