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rudra333
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\[\cos ^{-1}(\sin \frac{ 11\pi }{ 6 })\]
rudra333
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@satellite73
rudra333
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@satellite73 plz help
zugzwang
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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?
rudra333
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the answer is 2pi/3 ??
zugzwang
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seems like it
rudra333
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@satellite73
zugzwang
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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
\[x = -\frac{4\pi}{3}+2\pi=\frac{2\pi}{3}\]
rudra333
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k thanks but this other one is hard \[\tan(\sin ^{-1}-\frac{ 5 }{ 13 }\]
rudra333
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)
zugzwang
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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?
alanli123
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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.
rudra333
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but i how do i do that?
alanli123
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answer is 5/12 by the way
alanli123
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|dw:1358823550014:dw|
alanli123
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so... tan of theta is ?
rudra333
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how did u get 12? and one is negative
alanli123
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oops didn't catch the negative
alanli123
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so if its negative then it means the angle is either in the third or fourth quadrant
alanli123
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however my answer would still be correct if the angle was in the 3rd quadrant
rudra333
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@zaynahf
rudra333
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omg still confused
zaynahf
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Im sorry, i dont know how to work this out.
rudra333
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k :(
alanli123
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did the problems include restrictions?
rudra333
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yes
alanli123
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what were they?
rudra333
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but that's all the questions says
alanli123
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?? so is there or is there no restrictions like 180<theta<270 (for exmaple)
alanli123
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@satellite73 help!!
rudra333
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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
alanli123
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alright... shoot gimme another question
rudra333
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it is k i am doing graphing