anonymous
  • anonymous
a math question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\cos ^{-1}(\sin \frac{ 11\pi }{ 6 })\]
anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
@satellite73 plz help

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

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