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

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mathteacher1729
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry I mean \[\huge \arctan\left( \tan (6\pi/7) \right) \] or \[\huge \tan^{1}\left( \tan (6\pi/7) \right) \]

ashleedean12
 2 years ago
Best ResponseYou've already chosen the best response.0\[\tan^{1} [\tan (6\pi/7)]\]

mathteacher1729
 2 years ago
Best ResponseYou've already chosen the best response.0What do you know about inverse functions? (they're super important to answering this question).

ashleedean12
 2 years ago
Best ResponseYou've already chosen the best response.0um 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...

mathteacher1729
 2 years ago
Best ResponseYou've already chosen the best response.0The 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.

ashleedean12
 2 years ago
Best ResponseYou've already chosen the best response.0so would the answer just be 6pi/7 since the inverse tan would undo tan?

ashleedean12
 2 years ago
Best ResponseYou've already chosen the best response.0thanks (: does that apply to any function that has the inverse of the same function on the outside?

mathteacher1729
 2 years ago
Best ResponseYou've already chosen the best response.06pi/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. :)

ashleedean12
 2 years ago
Best ResponseYou've already chosen the best response.0what if it was something like \[\tan [\tan^{1}(\pi/10)] \]

ashleedean12
 2 years ago
Best ResponseYou've already chosen the best response.0the simplified version of 6pi/7 would be just pi/7 ?

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

phi
 2 years ago
Best ResponseYou've already chosen the best response.1the 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

ashleedean12
 2 years ago
Best ResponseYou've already chosen the best response.0the problem says simplify and use pi as needed..

phi
 2 years ago
Best ResponseYou've already chosen the best response.1In that case, the answer is 6 pi/7 (about 154.29º)

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

ashleedean12
 2 years ago
Best ResponseYou've already chosen the best response.0ok thank you sooo much ! i have test on this tomorrow and i had no clue how to do it! you are a lifesaver!
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