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**1. Homework Statement**

i was reading this book for school called investigating change and i was really lost on question 4:

tides of an area and their times are as follows:

high tide: low tide

1.64m 12:08am 0.4m 6:03 am

2.32m 12:46 PM 0.57m 7:33PM

1.59m 1:06am 0.49m 6:59am

2.26m 1:41PM 0.56m 8:33PM

a) find the average levels of high and low tides and average time between high tides. use this data to find a sine or cosine function to fit the data as well as possible. Note: the independent variable needs to be a real number, not a number of hours or minutes.

b) graph the data from the table and the function you have found on the same axes.

c)calculate the differences between the data and your model and try to find a function that fits these differences fairly well.

**2. Homework Equations**

y = A cos(Bx + C) + D

**3. The Attempt at a Solution**

average high tide: 1.9525m

low tide: 0.505m

time between high tide: 12 hours and 31 minutes

easy enough. what i have trouble with is the functions. iam guessing that the function will be a cos function since tides have to start off at a point where as sine starts from 0.

amplitude iam guessing will be: (ave high tide - ave low tide)/2 = 0.72375

and from that the mean value (in other words d) will be: (amplitude + avg low tide)= 1.22875

but i cant determine the period (b) or the phase shift (c)

also, iam lost to the point that i dont know how to make the equation for part a without a time variable. and have i started the part c question first with this equation planning or part a equation? is the time variable the only difference between the two?

i'll appreciate any help, thanks :)