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## Lulu212 3 years ago Solve sin2x + 4sin x + 3 = 0

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1. Lulu212

do u know how to solve this ?

2. jeanlouie

sin(2x) is more interesting :)

3. Omniscience

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

4. Omniscience

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

5. ash2326

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

6. Lulu212

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. Yahoo!

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

11. Yahoo!

@UnkleRhaukus @Hero @jim_thompson5910 @myininaya

12. Yahoo!

@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. Yahoo!

@satellite73 @saadi

15. Hero

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

16. Yahoo!

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

17. Yahoo!

@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. Yahoo!

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

20. Yahoo!

@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. Yahoo!

then it is a quad eq

24. Yahoo!

we can find sinx

25. Hero

I'm inclined to agree with @Mimi_x3

26. manishsatywali

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

27. nickhouraney

it cant be solved just endless ways of writing the equation

28. panlac01

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. panlac01

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. nickhouraney

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. panlac01

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. nickhouraney

@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. panlac01

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. panlac01

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

46. Hero

Well, Einstein's lost twin

47. nickhouraney

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. nickhouraney

it is

50. Hero

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

51. panlac01

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. panlac01

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

54. nickhouraney

same difference hero lol

55. UnkleRhaukus

twins dont necessarily have the same charistics

56. panlac01

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. panlac01

where's David Hume?

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