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Trigonometry: Graphing cos

  1. Nov 7, 2015 #1
    Hey I need a second opinion to see if my formulas and calculations are correct. Also I need help with graphing this problem.

    My problem is to find amplitude, period, horizontal shift, vertical translation, step and then graph of:

    y= 2 - (1/3) cos ( πx + (3π/2) ) , -1/4 ≤ x ≤ 15/4

    Using the formula:

    y = A cos ( Bx + C) + D

    A = 2

    B = π

    C = 3/2

    D = 0

    Amplitude: |A| = 1/3
    Period: ((2π) / |B|) = 2
    Horizontal Shift: -C/B = (3/(2π))
    Vertical Translation: D = 0
    Step: ((2π)/2)/B = 1
     
  2. jcsd
  3. Nov 7, 2015 #2

    JBA

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    All of your data results appear to be correct.
    Mod edit: Some of the results are incorrect.
    What is the problem you are having with the graph?
     
    Last edited by a moderator: Nov 7, 2015
  4. Nov 7, 2015 #3
    I'm lost on what goes where on the graph.
     
  5. Nov 7, 2015 #4

    JBA

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    Do you know the general shape of a simple y=cos x curve?

    What method are you using to try to create this curve?

    Actually, upon review I have realized that your A = 2 and D = 0 values are in error but your amplitude is correct. Look at all of the equation modifiers again to see if you can identify the correct values for A & D

    Also review your C/B value with respect to π
     
    Last edited: Nov 7, 2015
  6. Nov 7, 2015 #5

    Mark44

    Staff: Mentor

    A is not 2 and D is not 0.
    Your amplitude and period are correct, but the horizontal shift and vertical translation are incorrect. I don't know what "step" means with regard to this problem. Is "step" half a period?
     
  7. Nov 7, 2015 #6
    Amplitude: |A| = 1/3
    Period: ((2π) / |B|) = 2
    Horizontal Shift: -C/B = - (3/(2π))
    Vertical Translation: D = 0
    Step: ((2π)/2)/B = 1

    I've made adjustments to Horizontal Shift by making it a negative number
    I put Vertical translation as 0 since there is no D in the problem.
    I'm not sure what step is but our teacher told us the formula for it.

    Is there something I am missing to find Vertical translation?
    Is there another name for "Step"?
    The formulas that were given to me for step are different for each function. Sin and Cos is: ((2π)/2)/B, Tan is (π/2)/B
     
  8. Nov 7, 2015 #7

    JBA

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    OK, your problem is thinking that D must be at the end of the equation. Reverse the equation order and see what that makes the value of D be.
     
  9. Nov 7, 2015 #8

    Mark44

    Staff: Mentor

    No, that's still wrong.
    Still wrong.
    What is B? What is C?
    Yes, there is.
    This is because the period of the basic, untransformed sine and cosine functions is ##2\pi##. The period for the basic tangent function is ##\pi##.
     
  10. Nov 7, 2015 #9
    I reversed the order and got 2!
    So Vertical Translation = 2

    I found B and C by factoring out p from:

    y= 2 - (1/3) cos ( πx + (3π/2) )

    factored form:

    y= 2 - (1/3) cos ( π ( x + (3/2) )

    from the formula: y = A cos ( Bx + C) + D
    B = π
    C = 3/2

    Formula for Horizontal Shift is - ( C / B )
    (3/2)/(π/1) = 3/(2π)

    I'm trying to find out whats missing, still trying to find. any hints?
     
  11. Nov 7, 2015 #10

    Mark44

    Staff: Mentor

    Yes
    No, the pattern in your formula is different.
    Formula: y = A cos(Bx + C)
    In your work, you factored out ##\pi## from both terms
    The formula is NOT A cos(B(x + C))
    This formula, which you are blindly applying, is for the equation y = A cos (Bx + C)
    From this formula, what is B and what is C?
     
  12. Nov 7, 2015 #11

    JBA

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    The vertical shift is 2; so now you have everything except a confirmed horizontal shift.

    Actually, you have to think in terms of radians, the simple answer is that C = 3π/2 = 1.5π = 270° such that when x = 0 then cos (0 + 270°) = -1 and with the vertical y offset = 2 the result is 2 -1 = 1 (the minimum height of the oscillation) and when x = .5 then cos (.5 + 1.5)π = 2π = cos 180° =0 and y = 2+0 = 2 (the centerline of the curve oscillation) and when x = 1, cos ( 1 +1.5)π = cos 2.5 = cos 90° = 1 and y = 2+1 = 3 ( the maximum height of the oscillation), etc
     
    Last edited: Nov 8, 2015
  13. Nov 8, 2015 #12

    JBA

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    One clarification on the above, all of the above max/ min values of 1 & -1 are before muliplying the results of the cos by 1/3 as required by the total equation so for the purposes of your calculations and graph the results are actually 2 - 1/3 x 1 = 1.666, 2 - 1/3 x 0 = 2 and 2 - 1/3 X -1 = 2 + 1/3 = 2.333.
     
  14. Nov 8, 2015 #13
    B = πx
    C = 3π/2
    Horizontal Shift = -(3/2)!
    My book says that I have to factor out the coefficient of π before finding amplitude, period, etc.
     
    Last edited: Nov 8, 2015
  15. Nov 8, 2015 #14

    JBA

    User Avatar

    B = π not πx
     
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