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Cosine function & Modelling Tides

  1. Aug 2, 2008 #1
    I'm having a bit of trouble working out the cosine function for the data I have on tide charts.
    1. The problem statement, all variables and given/known data
    I need to put the data provided into the cosine function y=acos(nx-b)+c

    Morning average high tide: 5.137 metres
    Morning average low tide: 1.29 metres
    Afternoon average high tide: 4.732 metres
    Afternoon average low tide: 1.35
    Average high tide: 4.93 metres
    Average low tide: 1.32 metres
    Average time between high tide: 12.18 hours
    Average time between low tides: 12.15 hours

    2. Relevant equations
    y=acos(nx-b)+c or y=Acos(Bx + C) + D

    3. The attempt at a solution
    Through research I know that amplitude, a, will be (average high tide - average low tide) / 2
    so amplitude = 1.805

    Period,n or B, will be average time between high tides, so 12.29

    Now, I know that these are correct, but I'm no quite sure why. Nor do I know what the phase shift, b or C, will be. I have a feeling that c or D will be (average high tide + average low tide) / 2 = 3.125, but once again dont know why..

    Any help would be most appreciated!

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Aug 2, 2008 #2
    Okay so the basic equation for the cosine function, as you have correctly is
    y = Acos(Bx + c) + D
    Where A is the amplitude
    B is called the angular frequency. It is the 2pi (period of the cosine function y = cos(x)) divided by T where T is the period of your function. T is just the distance of one "cycle".
    x is your x.
    c is your phase shift for x. This is because you see, the c is inside the entire cosine function, and this would add to your x. A positive phase shift means a phase **** to your left on the x axis and a negative phase shift means a phase shift to your right on the x axis.
    D is the phase shift on the y axis. Its just like another linear equation where the y intercept is c. However, for this function, just ignore the D first and graph it. After this, shift the function up or down by D on the y axis

    If you don't understand anything from ^, let me know.

    If my explanation wasn't sufficient, you might want to try:
  4. Aug 2, 2008 #3
    Thanks for the clarification physicsnoob93. So, taking what you said into account, the function would be

    Is that on the way to being correct? I'm just not sure what C should be...?

  5. Aug 2, 2008 #4
    Ok sorry but i'm not really looking at the values but what you have to do is compare the cosine function:
    y = cos(x) and your function.
    You have to compare how much the x changes between the cos(x) function and the your function. This is the phase shift in the x direction.
  6. Aug 2, 2008 #5
    K thanks for the help so far. If anyone else can help that would be greatly appreciated!

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