## MrCarey 2 years ago sin(arcsin(-11π/13) I'd really just like an explanation of this one.

1. MrCarey

I don't know why I'm forgetting how to do this, but it's been awhile and my final is coming up and I want a better understanding of it.

2. godorovg

do you know the init Circle?

3. MrCarey

Yep

4. godorovg

when you at look the unit circle what quard would Sin be in?

5. MrCarey

I see that it goes -11π, so I believe it's going clockwise around the unit circle and I think it gets to Q3.

6. godorovg

yes correct, so in the problem what does that tell you?

7. MrCarey

I don't know...hahaha, rephrase that maybe?

8. godorovg

from looking at this problem and taking the information you already have what would you say the answer is? sin(arcsin(-11π/13)

9. godorovg

do you understand arcsin and what that means??

10. MrCarey

crap, I wrote it down wrong. It was arcsin(sin(-11π/13))

11. MrCarey

I have a pretty good understanding of how to use it. I'm rusty, though.

12. godorovg

okay, let us take this and break it down on what you know, you start I will fill in if needed.

13. MrCarey

I believe sin(ø) = arcsin (-11π/13) in this situation.

14. godorovg

you are right, but how did you do that?

15. MrCarey

I just kind of have that memorized. I guess I never really grasped that...

16. godorovg

okay, now I have a stupid what is the question asking for??? I am a little lost with the question here does it ask to solve or what?

17. MrCarey

Find the exact value of the given expression. Simplify your answer (rationalize the denom)

18. MrCarey

I also have that the answer is -2π/13

19. MrCarey

I don't really understand where the 2π comes from.

20. godorovg

because recall the unit circle has a total of 360 degrees right?

21. MrCarey

Yep and 2π is 360º

22. godorovg

2/pie is a point on the Unit the circle in which the angle is 360.. you beat to that one good job

23. MrCarey

So, my picture shows the line -11π/13 and the distance between that line and the 180º line is 2π/13.

24. MrCarey

Having a hard time understanding why it's 2π and not just π.

25. MrCarey

Probably just overthinking it.

26. godorovg

what I am questioning here the negative here in this case?

27. godorovg

because you start with a negative you will most likely end that way..

28. godorovg

2pie is at the 360 degrees which has points 0,0 so how can that be a negative result help here?

29. MrCarey

One sec, gonna post a photo of what is giving me a headache.

30. godorovg

I think we are both getting the same headache on this. This problem is going down..

31. MrCarey

Hahaha, I'm tellin' you. I haven't had any problems with any other questions, but this one is just destroying my brain.

32. godorovg

yeah, the same thing only that my brain is dead because I am stuying Vectors myself.

33. godorovg

what I am missing here????

34. lgbasallote

is the question still $\sin (arcsin (-11 \pi/3)$

35. MrCarey

arcsin(sin(-11π/3))

36. godorovg

37. MrCarey

Messed up the on the original post

38. lgbasallote

here's a hint.. arcsin( sin x) = x sin (arcsin x) = x cos( arc cos x) = x arc cos (cos x) = x tan (arctan x) = x arctan (tan x) = x does that help?

39. MrCarey

40. MrCarey

There is the picture that I was trying to describe.

41. MrCarey

I wish that helped, but I still can't figure out why it is -2π/13

42. lgbasallote

is that included in the question? or is that your solytion?

43. MrCarey

Solution. It's an answer key and I'm trying to decipher it.

44. MrCarey

I know it is -2π/13 because of the range, but I don't know where the 2π came from.

45. lgbasallote

use the hint i gave you...here's a demo $\sin (\sin^{-1} ( \frac{\pi}{2} ) ) = \frac{\pi}{2}$ $\sin^{-1} (\sin ( \frac{2 \pi}{5} ) ) = \frac{2 \pi}{5}$ getting it now?

46. lgbasallote

$\sin^{-1} (\sin ( \frac{-11\pi}{3} ) ) = -\frac{11\pi}{3}$ then simplify that you get $-\frac{2\pi}{3}$ make sense?

47. godorovg

lgbasallote what did I miss here? I mean I thought for sure I was going the right way what did I do in my steps that went wrong here? Help me to understand..

48. MrCarey

How'd you simplify to that?

49. lgbasallote

i think i wrote the wrong thingies lol...

50. lgbasallote

but that's the concept

51. MrCarey

Yeah, I knew what you were saying with the others. It's this deal here. I don't understand how it is simplifying from 11π to 2π.

52. MrCarey

It's like it just magically disappears.

53. lgbasallote

reference angles

54. MrCarey

Heh, I feel dumb for not knowing still.

55. godorovg

Mrcarey I am so sorry I took the long way here.

56. MrCarey

Haha, no problem at all. I've been at it for so long, it didn't even feel that long.

57. godorovg

ha ha yeah better next time right? HA HA..

58. MrCarey

Exactly! Thanks for trying at least. Good luck with the vector calc. I'll be THERE soon enough.

59. godorovg

I am Physics Engineering major myelf

60. MrCarey

Mech E. for me. Math math math math and more math!

61. godorovg

you got this now

62. MrCarey

Yeah, I feel better about it. Got one more day of review in class, so I'll probably bring it up with him anyway. Thanks again!

63. godorovg

do you another problem you need help on? Just asking here

64. MrCarey

Nope, this one seemed to be the only one I kept coming back to. This stupid thing made everything else seem easy!

65. godorovg

yeah, I only hope for me it is just one problem that will allow everything to be easy after that. Fat chance ha ha

66. MrCarey

Hahahaha, no way. I've peeked at that stuff and needed to take a nap after.

67. godorovg

did that one already.. I took a 5hrs nap

68. godorovg

I am doing Calc1 andPhysics 1 with Calc

69. MrCarey

I'll be doing that in the Fall. Well, no Physics yet, couldn't get in the class. General Chem 1 and Calc 1. Gonna be exciting.

70. godorovg

what school?

71. MrCarey

Doing community for now, so I can transfer to University of Washington Seattle.

72. MrCarey

You?

73. godorovg

cool I live Iin Portland Ore myself..

74. godorovg

I will start Sept 24th at Jr College than transfer to Tarleton ST university in TX in Spring 2013

75. MrCarey

Awesome, TX should be pretty fun. Definitely a change of scenery.

76. godorovg

I am studying math and Physics by watching videos and taking notes on my own

77. MrCarey

78. godorovg

yeah StephenVille is very small town though

79. godorovg

who is Khan A?

80. MrCarey

www.khanacademy.com MIT grad who made his own site that teaches every kind of math and most sciences.

81. MrCarey

Free site for learning. I've used it for awhile now. Especially when I get bad professors.

82. godorovg

funny you just posted MIT, Because I am using thier open courses on line for the video in math and Physics

83. MrCarey

Haha, that works, too! You'd probably like his teaching style. He is very helpful and has tons of videos. I always recommend the site.

84. godorovg

thanks will check it out, hey you have a great night and if you need me to help me message me

85. godorovg

you

86. MrCarey

Sounds like a plan! Have a good night!

87. godorovg

you too.