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

1. MrCarey Group Title

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 Group Title

do you know the init Circle?

3. MrCarey Group Title

Yep

4. godorovg Group Title

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

5. MrCarey Group Title

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 Group Title

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

7. MrCarey Group Title

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

8. godorovg Group Title

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 Group Title

do you understand arcsin and what that means??

10. MrCarey Group Title

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

11. MrCarey Group Title

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

12. godorovg Group Title

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

13. MrCarey Group Title

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

14. godorovg Group Title

you are right, but how did you do that?

15. MrCarey Group Title

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

16. godorovg Group Title

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 Group Title

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

18. MrCarey Group Title

I also have that the answer is -2π/13

19. MrCarey Group Title

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

20. godorovg Group Title

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

21. MrCarey Group Title

Yep and 2π is 360º

22. godorovg Group Title

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 Group Title

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

24. MrCarey Group Title

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

25. MrCarey Group Title

Probably just overthinking it.

26. godorovg Group Title

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

27. godorovg Group Title

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

28. godorovg Group Title

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

29. MrCarey Group Title

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

30. godorovg Group Title

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

31. MrCarey Group Title

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 Group Title

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

33. godorovg Group Title

what I am missing here????

34. lgbasallote Group Title

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

35. MrCarey Group Title

arcsin(sin(-11π/3))

36. godorovg Group Title

37. MrCarey Group Title

Messed up the on the original post

38. lgbasallote Group Title

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 Group Title

40. MrCarey Group Title

There is the picture that I was trying to describe.

41. MrCarey Group Title

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

42. lgbasallote Group Title

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

43. MrCarey Group Title

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

44. MrCarey Group Title

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

45. lgbasallote Group Title

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 Group Title

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

47. godorovg Group Title

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 Group Title

How'd you simplify to that?

49. lgbasallote Group Title

i think i wrote the wrong thingies lol...

50. lgbasallote Group Title

but that's the concept

51. MrCarey Group Title

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 Group Title

It's like it just magically disappears.

53. lgbasallote Group Title

reference angles

54. MrCarey Group Title

Heh, I feel dumb for not knowing still.

55. godorovg Group Title

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

56. MrCarey Group Title

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

57. godorovg Group Title

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

58. MrCarey Group Title

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

59. godorovg Group Title

I am Physics Engineering major myelf

60. MrCarey Group Title

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

61. godorovg Group Title

you got this now

62. MrCarey Group Title

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 Group Title

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

64. MrCarey Group Title

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

65. godorovg Group Title

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 Group Title

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

67. godorovg Group Title

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

68. godorovg Group Title

I am doing Calc1 andPhysics 1 with Calc

69. MrCarey Group Title

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 Group Title

what school?

71. MrCarey Group Title

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

72. MrCarey Group Title

You?

73. godorovg Group Title

cool I live Iin Portland Ore myself..

74. godorovg Group Title

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

75. MrCarey Group Title

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

76. godorovg Group Title

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

77. MrCarey Group Title

78. godorovg Group Title

yeah StephenVille is very small town though

79. godorovg Group Title

who is Khan A?

80. MrCarey Group Title

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

81. MrCarey Group Title

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

82. godorovg Group Title

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

83. MrCarey Group Title

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 Group Title

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

85. godorovg Group Title

you

86. MrCarey Group Title

Sounds like a plan! Have a good night!

87. godorovg Group Title

you too.