Inverse trig function Watch

coconut64
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#1
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Can someone explain how to tackle these kind of questions. I don't really understand why although having done it already...

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RDKGames
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(Original post by coconut64)
Can someone explain how to tackle these kind of questions. I don't really understand why although having done it already...
what do you do with tube arc part? I don't quite get it thanks.
Tube arc part? What???

I don't understand what your question is.
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will'o'wisp
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(Original post by coconut64)
Can someone explain how to tackle these kind of questions. I don't really understand why although having done it already...

Name:  14786047882601123063672.jpg
Views: 34
Size:  311.5 KB what do you do with tube arc part? I don't quite get it thanks.
u dun fine tho??

What do you not understand?
1.Remove arc
2.All x on one side
3.Solve for x
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coconut64
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(Original post by RDKGames)
Tube arc part? What???

I don't understand what your question is.
So I am unsure as to why you would get rid of the acrtan part on the left by multiplying the right hand side by tan.

Thanks
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coconut64
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(Original post by will'o'wisp)
u dun fine tho??

What do you not understand?
1.Remove arc
2.All x on one side
3.Solve for x
Hi thanks for the help. I just don't realy understand how you can just get rid of the arctanx on the left by adding tan on the right hand side.

Thanks
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will'o'wisp
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(Original post by coconut64)
Hi thanks for the help. I just don't realy understand how you can just get rid of the arctanx on the left by adding tan on the right hand side.

Thanks
I see do you understand what arc means? Similar thing with a log

\theta=arctanx

tan \theta=x
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NotNotBatman
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You know from functions that  f(f^-1(x)) = x that is a function composed with it's inverse is the identity function and the result is just the argument (what's in the brackets). Arctan x is the inverse of tanx so arctan(tan(x)) = x, so in your question tan(arctan(x-2)) =x-2.

You're not multiplying by tan, you have to have the tan of something. You're composing the inverse on both sides.
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the bear
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tan and arctan are inverse functions... so if you do both they "cancel out"...

tan(arctan( W )) is always W

arctan(tan ( W )) is always W
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RDKGames
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(Original post by coconut64)
Hi thanks for the help. I just don't realy understand how you can just get rid of the arctanx on the left by adding tan on the right hand side.

Thanks
You're not "adding" tan to both sides. You are taking tan of both sides and since \arctan is a more acceptable notation of \tan^{-1} you essentially get \tan(\tan^{-1}(x-2))=\tan(-\frac{\pi}{3}) and since tan and inverse tan are both opposite operations of each other, they cancel out. It's like saying "divide this number by 5 and then multiply the result by 5" so 5(\frac{x}{5})=x since the operations on the LHS cancel.

More formally f(f^{-1}(x))=x for a suitable domain which makes f(x) an injective function (ie, one-to-one)
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coconut64
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Thanks everyone
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