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arctan(tan7)=2pi -7 why?? i m confused....

arctan(tan7)=2pi





-7


why??




i m confused....

Grade:

2 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

the range of the arctan function is (-π/2,π/2)

in addition, tan(theta)=nπ+ (-1)narctan(theta), where 'n' is any integer.

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Shreya,

 

Please note that tan-1t has range between -Π/2 and +Π/2.

 

So tan-1tanx = x ----------- when -Π/2 < x < +Π/2-------(1)

 

So tan-1tan7 = tan-1(-tan(2Π-7) = tan-1tan(7-2Π)-------- {Now note 7-2Π lies in the given interval of (1)}.

 

And hence the answe is 7-2Π, and it is not 2Π-7.

 

Hope that helps.

 

All the best,

Regards,

Ashwin (IIT Madras)

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