Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By romsek

Thread: URGENT Parametrics

  1. #1
    Junior Member
    Joined
    Dec 2013
    From
    U.S.
    Posts
    30

    URGENT Parametrics

    Let be the graph of the parametric equations





    What is the length of the smallest interval
    such that the graph of these equations for all produces the entire graph ?
    Last edited by orange; Dec 18th 2013 at 07:25 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    4,540
    Thanks
    1865

    Re: URGENT Parametrics

    Quote Originally Posted by orange View Post
    Let be the graph of the parametric equations





    What is the length of the smallest interval
    such that the graph of these equations for all produces the entire graph ?
    Cos[4t] needs (2pi)/4 = pi/2

    Sin[6t] needs (2pi)/6 = pi/3

    what's the least common multiple of 1/2 and 1/3 ? So what's the minimum interval needed for a full cycle?
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2013
    From
    U.S.
    Posts
    30

    Re: URGENT Parametrics

    1 is their LCM. So I guess the minimum interval is just pi?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    4,540
    Thanks
    1865

    Re: URGENT Parametrics

    give that man a kewpie doll!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    846

    Re: URGENT Parametrics

    Hello, orange!

    I "eyeballed" the problem.
    I think I have the solution.


    Let G be the graph of the parametric equations: . \begin{Bmatrix}x &=& \cos(4t) \\ y &=& \sin(6t)\end{Bmatrix}

    What is the length of the smallest interval I such that the graph
    of the equations for all t \in I produces the entire graph of G ?

    When t = 0\!:\;\begin{Bmatrix}x &=& \cos(0) &=& 1 \\ y &=& \sin(0) &=& 0\end{Bmatrix}

    At the "start", the graph is at (1,0).


    Here is what I found:

    . . \begin{array}{c|c|c|} t & \cos(4t) & \sin(6t) \\ \hline 0 & 1 & 0 \\ \frac{\pi}{4} & \text{-}1 & \text{-}1 \\ \frac{\pi}{2} & 1 & 0 \\ \frac{3\pi}{4} & \text{-}1 & 1 \\ \hline \pi & 1 & 0 \\ \vdots & \vdots & \vdots\end{array}

    . . and the cycle repeats.


    Therefore: . I \,=\,[0,\,\pi]
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    1,028
    Thanks
    408

    Re: URGENT Parametrics

    Hi,
    If a given parametric curve is periodic, finding its period is a mystery to me. Here's a problem that I tackled some time ago with its solution; you might try your hand at it (my proof was somewhat long and involved). I wish I knew some general procedure to find the period of such periodic functions.

    URGENT Parametrics-mhfcalc26.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. parametrics!
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Aug 8th 2010, 05:16 PM
  2. Parametrics Help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 10th 2009, 11:17 AM
  3. Parametrics.....
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 25th 2009, 03:22 PM
  4. parametrics!
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Jan 6th 2009, 02:50 AM
  5. Parametrics
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Apr 8th 2008, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum