a math question

- anonymous

a math question

- chestercat

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- anonymous

\[\cos ^{-1}(\sin \frac{ 11\pi }{ 6 })\]

- anonymous

@satellite73

- anonymous

@satellite73 plz help

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## More answers

- zugzwang

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?

- anonymous

the answer is 2pi/3 ??

- zugzwang

seems like it

- anonymous

@satellite73

- zugzwang

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
\[x = -\frac{4\pi}{3}+2\pi=\frac{2\pi}{3}\]

- anonymous

k thanks but this other one is hard \[\tan(\sin ^{-1}-\frac{ 5 }{ 13 }\]

- anonymous

)

- zugzwang

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

- anonymous

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

- anonymous

but i how do i do that?

- anonymous

answer is 5/12 by the way

- anonymous

|dw:1358823550014:dw|

- anonymous

so... tan of theta is ?

- anonymous

how did u get 12? and one is negative

- anonymous

oops didn't catch the negative

- anonymous

so if its negative then it means the angle is either in the third or fourth quadrant

- anonymous

however my answer would still be correct if the angle was in the 3rd quadrant

- anonymous

@zaynahf

- anonymous

omg still confused

- anonymous

Im sorry, i dont know how to work this out.

- anonymous

k :(

- anonymous

did the problems include restrictions?

- anonymous

yes

- anonymous

what were they?

- anonymous

but that's all the questions says

- anonymous

?? so is there or is there no restrictions like 180

- anonymous

@satellite73 help!!

- anonymous

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

- anonymous

alright... shoot gimme another question

- anonymous

it is k i am doing graphing

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