May 16th, 2017, 11:31 AM  #1 
Member Joined: Dec 2016 From:  Posts: 44 Thanks: 7  Formula of arctan(tan(x))
Does the formula $\arctan(\tan(x))=x$ hold only for $x\in(\pi/2,+\pi/2)$, and how can this be extended to other values of x? Thanks!

May 17th, 2017, 03:07 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,405 Thanks: 611 
Since tan(x) is not a "one to one" function, strictly speaking it does not have an inverse function so we restrict it to one "period", between and . Then arctan is defined as giving a value between those.


Tags 
arctantanx, formula 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Arctan identity  moshelevi33  Trigonometry  7  November 12th, 2016 05:26 AM 
cos(arctan(4/3)arcsin(24/25)...  mared  Trigonometry  2  May 17th, 2014 11:45 AM 
arctan...  ungeheuer  Calculus  3  January 16th, 2013 05:17 AM 
arctan  danneman91  Algebra  2  October 3rd, 2011 12:11 PM 
Solving arctan( k * x ) + x = c  HenrikAndresen  Complex Analysis  2  October 26th, 2009 12:22 AM 