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Homework Help: Phase Constant graph help

  1. Oct 10, 2007 #1
    all the solution is there, but i just don't understand the answer to part B.
    CIMG1818.jpg
    for part B, why is the sign negative?
     
  2. jcsd
  3. Oct 10, 2007 #2

    learningphysics

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    The graph is a cosine wave shifted to the right by an angle less than 90...

    So of your two solutions (+pi/3 -pi/3) for arccos, you need the one with the minus, for a right shift, as opposed to a left shift...
     
  4. Oct 10, 2007 #3

    Hootenanny

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    Remember that there are an infinte number of solutions to trigonometric equations, so in your case;

    [tex]\cos\phi = \frac{1}{2} \Rightarrow \phi = -\frac{\pi}{3}, \frac{\pi}{3}, \frac{5\pi}{3}...[/tex]

    [tex] \phi = \frac{\pi}{3} \pm 2\pi\cdot k \hspace{1cm}; k\in\mathbb{Z}[/tex]

    But the thing to remember here is that the phase angle is simply a translation along the x axis. A positive phase angle translates the curve in the negative x direction (to the left) and a negative phase angle translates the curve in the positive x direction (to the right).

    Now, in which direction do we need to translate the cosine curve so that is matches yours?

    Edit: Several mintues to slow ... :frown:
     
    Last edited: Oct 10, 2007
  5. Oct 10, 2007 #4
    thanks a lot learningphysics and house md
     
  6. Dec 13, 2009 #5
    I have iqbal too =O ubcccc
     
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