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Math Help - Graph y=4-3/4sec(3x-∏)

  1. #1
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    Graph y=4-3/4sec(3x-∏)

    Having some trouble with the phase shift of this problem.
    Graph y=4-3/4sec(3x-∏)
    I graphed cos first but the p.s. keeps me up at night. Any walk throughs would be appreciated!

    Thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    Is it y = 4 - \dfrac{3}{4 \sec(3x-\pi)} \text {  or  } y = 4-\dfrac{3\sec(3x-\pi)}{4}

    I would go one step at a time. If y=f(x) then

    f(3x) is f(x) compressed by a factor of 3 (in other words you'll complete 3 cycles in every 2pi radians)
    f(x-pi) is f(x) shifted pi units to the right on the x axis
    (3/4)f(x) is a vertical "stretch" of 3/4. For trig graphs this only really changes the extrema - in this case f(x) will vary between -3/4 and 3/4
    -f(x) is f(x) inverted/flipped in the x axis
    4-f(x) is f(x) shifted up the y axis by 4 units.

    If you confirm the equation in question I will graph these steps for you using software
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  3. #3
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    Sorry for Double post check down
    Last edited by linipopent; December 21st 2010 at 12:34 PM. Reason: Question Worded Better
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  4. #4
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    Its the second equation.
    The equation had no parenthesis around the -3/4 (amplitude)
    The trouble I am having is dividing the P.S. into four equal parts.
    P.S. -d/b= ∏/3 (Start) Period 2∏/b=2∏/3 (End)
    What are the points in between?
    Last edited by linipopent; December 21st 2010 at 09:56 PM.
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  5. #5
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    e^(i*pi)'s Avatar
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    Your phase shift is \frac{\pi}{3}. Therefore if you draw the graph of \cos(3x) (I don't know if this is correct since I still don't know if sec(x) is in the numerator or denominator but cos was mentioned in the OP)

    From the graph of cos(3x) your phase shift will be \frac{\pi}{3} units in the positive direction of the x-axis. Essentially it maps each value of \theta to a value of \left(\theta, \theta+\frac{\pi}{3}\right) (I introduced theta to make it easier to understand)



    Spoiler:




    edit: with regards to the image the phase difference should be pi/3
    Last edited by e^(i*pi); December 22nd 2010 at 09:45 AM. Reason: added clear picture
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  6. #6
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    Sec(x) is in the numerator
    4 is the demoninator
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  7. #7
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    What are the x-axis values in between -2/pi to 2/pi and 2/pi to pi?
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