Cosine function & Modelling Tides

[flyinghigh]

I'm having a bit of trouble working out the cosine function for the data I have on tide charts.

Homework Statement

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

Homework Equations

y=acos(nx-b)+c or y=Acos(Bx + C) + D

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 don't know why..

Any help would be most appreciated!

flyinghigh

 

[physicsnoob93]

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:
http://www.zweigmedia.com/RealWorld/Calcsumm9.html

 

[flyinghigh]

Thanks for the clarification physicsnoob93. So, taking what you said into account, the function would be
y=1.805cos(2$$\pi$$/5x-??)+3.125

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

flyinghigh

 

[physicsnoob93]

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.

 

[flyinghigh]

K thanks for the help so far. If anyone else can help that would be greatly appreciated!

flyinghigh