Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Inverse Tangent's y limit?

  1. Aug 11, 2016 #1
    When I was experimenting with graphing functions, I noticed the inverse tangent, or arctanget, curves away from y=2, or may be less. What is the y limit for the inverse tangent function? Does it for ever increase, or terminate at a co-ordinate?
  2. jcsd
  3. Aug 11, 2016 #2


    User Avatar
    Science Advisor
    Education Advisor

    First graph the function ##\tan## on the real line. Is it defined everywhere? Then recall that ##\arctan## is defined as the inverse of the restriction of ##\tan## to the interval ##(-\tfrac{\pi}{2},\tfrac{\pi}{2})##. (Why is it necessary to first restrict ##\tan##?) Finally try to answer your own question.
    Last edited: Aug 11, 2016
  4. Aug 11, 2016 #3


    User Avatar
    Homework Helper

    Little correction: you should exclude pi/2 and -pi/2 from the interval as tan is not defined for those values.
  5. Aug 12, 2016 #4
    I approximately understand. So by your logic, when you graph y=tan(x), when it goes up and approaches endlessly, it stops round about π/2 and goes back down to increase and repeat this process? My original question was when does it stop on the y axis? It is infinity? However, when I apply this in my calculator.
    tan(π/2)≈0.027 (2sf)
    This does not make sense; when I graph this using a software. The line does not define this? when I observe the x=π/2 is does not intersect tan at 0.027? I am missing something?

    Thanks in advance,
  6. Aug 12, 2016 #5


    User Avatar
    Homework Helper

    You should put your calculator ib radian mode, not degree mode, if you do not have done this yet. tan(pi/2) must give an error, otherwise you or your calculator are doing something wrong.
  7. Aug 12, 2016 #6
    Okay thanks, that worked. Thinking immaterially, correct me if I am invalid, when π/2 subtract an infinitesimal, tan function would equal what one would interpret as infinity?
    Let i="infinitesimal"

    However, thanks for your help, I now understand things better.
  8. Aug 13, 2016 #7


    User Avatar
    Homework Helper

    I don't like to talk about infinitesimals, however:

    lim x-> + infinity arctan(x) = pi/2
  9. Aug 13, 2016 #8


    User Avatar
    Science Advisor

    Hey LtIvan,

    You should define the y-limit mathematically and evaluate it using limit laws.

    If something increases forever then the derivative is greater than zero.

    Evaluating functions are easy if you define them consistently, correctly, and concisely.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Inverse Tangent's y limit?