00:01
So here we have a maximum value of 3 .4, a minimum value of negative 3 .4, and the max occurs at 0 and at 12 and at 24, and the min occurs at 6 and 18.
00:29
And our midline then is going to be whatever is in the middle between those two.
00:36
So midline is at y is equal to 0.
00:41
And if we want to write this as a function of the cosine, well, the cosine of 0 is 1, so that's the maximum value.
00:57
Your amplitude here then is is, let's see here, 3 .4.
01:08
And our period, it takes 12 hours to go from the max to the min and back to the max, so period is 12 hours.
01:23
That means that this is our b, and we want to write f of t is equal to a times the cosine of bt minus c plus d.
01:46
Well, our d, our midline is 0, so our d is 0.
01:52
The difference between the max and the midline is a is your amplitude, and then, let's see here, your period is 12 hours, so then b is equal to 2 pi over, period is equal to 2 pi over b...