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inverse tan[tan(6pi/7)]
i need an exact answer using pi as needed. can someone explain to me how to solve this?
 one year ago
 one year ago
inverse tan[tan(6pi/7)] i need an exact answer using pi as needed. can someone explain to me how to solve this?
 one year ago
 one year ago

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mathteacher1729Best ResponseYou've already chosen the best response.0
Sorry I mean \[\huge \arctan\left( \tan (6\pi/7) \right) \] or \[\huge \tan^{1}\left( \tan (6\pi/7) \right) \]
 one year ago

ashleedean12Best ResponseYou've already chosen the best response.0
\[\tan^{1} [\tan (6\pi/7)]\]
 one year ago

mathteacher1729Best ResponseYou've already chosen the best response.0
What do you know about inverse functions? (they're super important to answering this question).
 one year ago

ashleedean12Best ResponseYou've already chosen the best response.0
um i know how to put them in my calculator and that they have restrictions this particular one the answer must be in either quadrant 1 or 4...
 one year ago

mathteacher1729Best ResponseYou've already chosen the best response.0
The key is that an inverse function "undoes" a function. arctan ( tan ( stuff ) ) = stuff and tan ( arctan ( stuff ) ) = stuff (assuming domains and ranges are valid) also \(\large \arctan(x) = \tan^{1}(x) \) it's just notation. They mean the same exact thing.
 one year ago

ashleedean12Best ResponseYou've already chosen the best response.0
so would the answer just be 6pi/7 since the inverse tan would undo tan?
 one year ago

ashleedean12Best ResponseYou've already chosen the best response.0
thanks (: does that apply to any function that has the inverse of the same function on the outside?
 one year ago

mathteacher1729Best ResponseYou've already chosen the best response.0
6pi/7 or pi/7, they are the same thing. And yes, inverse function ( function ( stuff ) ) = stuff function ( inverse function ( stuff ) ) = stuff Inverse functions and functions "undo" each other. That's glossing over a lot of details, but that's the big idea. :)
 one year ago

ashleedean12Best ResponseYou've already chosen the best response.0
what if it was something like \[\tan [\tan^{1}(\pi/10)] \]
 one year ago

ashleedean12Best ResponseYou've already chosen the best response.0
the simplified version of 6pi/7 would be just pi/7 ?
 one year ago

phiBest ResponseYou've already chosen the best response.1
yes, pi/10 you can check with your calculator tan^1 (pi/10) you are treating pi/10 as a number not as an angle.
 one year ago

phiBest ResponseYou've already chosen the best response.1
the simplified version of 6pi/7 would be just pi/7 ? I would not say "simplified" If you mean Is pi/7 the "reference angle" of 6pi/7, that is true
 one year ago

ashleedean12Best ResponseYou've already chosen the best response.0
the problem says simplify and use pi as needed..
 one year ago

phiBest ResponseYou've already chosen the best response.1
In that case, the answer is 6 pi/7 (about 154.29º)
 one year ago

phiBest ResponseYou've already chosen the best response.1
unless they want the answer between pi/2 and pi/2 in which case they want pi/7 (see math teacher's post)
 one year ago

ashleedean12Best ResponseYou've already chosen the best response.0
ok thank you sooo much ! i have test on this tomorrow and i had no clue how to do it! you are a lifesaver!
 one year ago
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