Results 1 to 2 of 2

Math Help - Equation

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    62

    Equation

    Hi,

    I must show that (\forall k \in \mathbb{Z}) \forall x \in ]-\frac{\pi}{2}+k\pi;\frac{\pi}{2}+k\pi[: Arctan(tanx)=x-k\pi.

    I know just that Arctan(tanx)=x when x \in  ]-\frac{\pi}{2}+k\pi;\frac{\pi}{2}+k\pi[

    Can you help me???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by lehder View Post
    Hi,

    I must show that (\forall k \in \mathbb{Z}) \forall x \in ]-\frac{\pi}{2}+k\pi;\frac{\pi}{2}+k\pi[: Arctan(tanx)=x-k\pi.

    I know just that Arctan(tanx)=x when x \in ]-\frac{\pi}{2}{\color{red}+k\pi};\frac{\pi}{2}{\col  or{red}+k\pi}[
    No, I think that's wrong (and contradicts what you are required to prove). Instead, you know that Arctan(tanx)=x when x \in ]-\frac{\pi}{2};\frac{\pi}{2}[

    And then you know something more: you know that \tan has period \pi, therefore you can add / subtract \pi an integral number of times until the value of an x\in]-\frac{\pi}{2}+k\pi;\frac{\pi}{2}+k\pi[ actually lies in ]-\frac{\pi}{2};+\frac{\pi}{2}[.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 11th 2011, 02:17 AM
  2. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 12:39 PM
  3. Replies: 2
    Last Post: May 18th 2009, 01:51 PM
  4. Replies: 2
    Last Post: April 28th 2009, 07:42 AM
  5. Replies: 1
    Last Post: October 23rd 2008, 04:39 AM

Search Tags


/mathhelpforum @mathhelpforum