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

mathteacher1729
 one year 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
 one year 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
 one year 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
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0what if it was something like \[\tan [\tan^{1}(\pi/10)] \]

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

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

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

phi
 one year 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
 one year 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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