In Bear Creek Bay in July, high tide is at 1:00 pm. The water level at

high tide is 7 feet at high tide and 1 foot at low tide. Assuming the

next high tide is exactly 12 hours later and the height of the water can

be modeled by a cosine curve, find an equation for Bear Creek Bay's

water level in July as a function of time.

The reason we use cosine, is because a cosine graph is at its maximum at the beginning of the cycle.

We begin with basic cosine equation:

Y (x) = Acos (Bx+c) + D

First we need to determine the middle line of the graph (amplitude) by finding the difference between tides and dividing by two: (7-1) / 2=3

We know that period is 12. This means that b needs to be pi/6 or 0.523 if 12b=2pi

Then we need to average out the tides, to determine how much the curve needs to shift: (7+1) / 2 = 4

In addition, we need to shift the equation to the right since high tide is at 1pm or 13 hours after midnight.

In the end we get the following equation:

y=4+3cos (0.523 (x-13))