Results 1 to 4 of 4

Math Help - How to do: Phase Shift of tan

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    13

    How to do: Phase Shift of tan

    I was wondering how do i do the phase shift for




    all i know is:


    ?? 3x ??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello S2Krazy
    Quote Originally Posted by S2Krazy View Post
    I was wondering how do i do the phase shift for




    all i know is:


    ?? 3x ??
    The graph of y = \tan(\theta+ \tfrac{\pi}{6}) is the same as the graph of y =\tan(\theta), shifted a distance \tfrac{\pi}{6} to the left.

    If you want to see why, just look at the zero values.
    When \theta = 0, y=\tan(\theta)=\tan(0) = 0. So the graph 'starts' at (0,0).
    But when \theta=0, y=\tan(\theta+\tfrac{\pi}{6})=\tan(\tfrac{\pi}{6}). So this graph 'starts' at (0,\tfrac{\pi}{6}), and it's when \theta = -\tfrac{\pi}{6} that we get the value y = 0.
    Now if we multiply the independent variable by 3, and replace \theta with 3x, we get the graphs of y = \tan(3x) and y = \tan(3x+\tfrac{\pi}{6}). Now, in the second graph, we shall need to take 3x = -\tfrac{\pi}{6} to get our zero value of y. So that's x = -\tfrac{\pi}{18}. So the graph has now been shifted \tfrac{\pi}{18} to the left.

    Finally, note that multiplying by 5, to give y = 5\tan(3x+\tfrac{\pi}{6}), makes no difference to the phase-shift: it merely 'stretches' the graph in a vertical direction either side of the x-axis by a factor of 5.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    13
    ah icic cool thxs.

    so for



    the phase shift would be -4pi/5 correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Quote Originally Posted by S2Krazy View Post
    ah icic cool thxs.

    so for



    the phase shift would be -4pi/5 correct?
    Correct!

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Phase shift..
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 18th 2011, 12:45 AM
  2. phase shift
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: December 13th 2010, 06:04 PM
  3. Phase Shift
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: January 26th 2010, 09:34 AM
  4. phase shift
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 15th 2009, 07:58 PM
  5. Phase shift??
    Posted in the Trigonometry Forum
    Replies: 11
    Last Post: April 23rd 2007, 12:50 PM

Search Tags


/mathhelpforum @mathhelpforum