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rudra333

  • 3 years ago

a math question

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  1. rudra333
    • 3 years ago
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    \[\cos ^{-1}(\sin \frac{ 11\pi }{ 6 })\]

  2. rudra333
    • 3 years ago
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    @satellite73

  3. rudra333
    • 3 years ago
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    @satellite73 plz help

  4. zugzwang
    • 3 years ago
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    Play with the values for this one... Let \[x = \cos^{-1}(\sin \frac{11\pi}{6})\]and if we get the cosine of both sides, we are left with...\[\cos x = \sin \frac{11\pi}{6}\]perhaps it's simpler from here on in?

  5. rudra333
    • 3 years ago
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    the answer is 2pi/3 ??

  6. zugzwang
    • 3 years ago
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    seems like it

  7. rudra333
    • 3 years ago
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    @satellite73

  8. zugzwang
    • 3 years ago
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    You're right. Hang on... in general, \[\cos(\frac{\pi}{2} - \theta)=\sin(\theta)\] So \[\sin\frac{11\pi}{6}=\cos \left( \frac{\pi}{2}-\frac{11\pi}{6} \right)\] \[=\cos \left( -\frac{8\pi}{6} \right)\] It would appear \[x=-\frac{4\pi}{3}+2k\pi\] where k is any integer. But since we're talking angles, adding 360 degrees, or 2pi, would give the same angle. Consider doing that here, because that negative angle ain't pretty XD \[x = -\frac{4\pi}{3}+2\pi=\frac{2\pi}{3}\]

  9. rudra333
    • 3 years ago
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    k thanks but this other one is hard \[\tan(\sin ^{-1}-\frac{ 5 }{ 13 }\]

  10. rudra333
    • 3 years ago
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    )

  11. zugzwang
    • 3 years ago
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    It's a bit complicated, but think of it this way... the SINE of the angle is -5/13, so what is its TANGENT?

  12. alanli123
    • 3 years ago
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    here's what you do: sine of what angle will equal 5/13? Then you take that angle and take the tan of it.

  13. rudra333
    • 3 years ago
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    but i how do i do that?

  14. alanli123
    • 3 years ago
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    answer is 5/12 by the way

  15. alanli123
    • 3 years ago
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    |dw:1358823550014:dw|

  16. alanli123
    • 3 years ago
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    so... tan of theta is ?

  17. rudra333
    • 3 years ago
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    how did u get 12? and one is negative

  18. alanli123
    • 3 years ago
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    oops didn't catch the negative

  19. alanli123
    • 3 years ago
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    so if its negative then it means the angle is either in the third or fourth quadrant

  20. alanli123
    • 3 years ago
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    however my answer would still be correct if the angle was in the 3rd quadrant

  21. rudra333
    • 3 years ago
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    @zaynahf

  22. rudra333
    • 3 years ago
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    omg still confused

  23. zaynahf
    • 3 years ago
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    Im sorry, i dont know how to work this out.

  24. rudra333
    • 3 years ago
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    k :(

  25. alanli123
    • 3 years ago
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    did the problems include restrictions?

  26. rudra333
    • 3 years ago
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    yes

  27. alanli123
    • 3 years ago
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    what were they?

  28. rudra333
    • 3 years ago
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    but that's all the questions says

  29. alanli123
    • 3 years ago
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    ?? so is there or is there no restrictions like 180<theta<270 (for exmaple)

  30. alanli123
    • 3 years ago
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    @satellite73 help!!

  31. rudra333
    • 3 years ago
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    no that is all the question says do u know the answer plz i am confused i will just do others if u don't know this

  32. alanli123
    • 3 years ago
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    alright... shoot gimme another question

  33. rudra333
    • 3 years ago
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    it is k i am doing graphing

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