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For this problem, we're told that the desert temperature, h, oscillates daily between 42 degrees fahrenheit at 4 a .m.
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And 82 degrees fahrenheit at 4 p .m.
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We are asked to write a possible formula for h measured in hours from 4am, where we are to use the form h equals a times cos of bt plus c.
00:20
So one thing that we can note here is that the total magnitude of our oscillation, our a value here, it's going to have to be equal to the distance between 82 degrees fahrenheit and 42 degrees fahrenheit, which is clearly 40.
00:37
So we have an amplitude or the amplitude of the oscillation will be 40.
00:42
Then we can note that the sort of midpoint in between 42 degrees fahrenheit and 82 degrees fahrenheit is going to be at 62 degrees fahrenheit.
00:54
So that's going to have to be our vertical offset, that c value.
00:59
Now, the one thing that is going to be a little bit complicating is that we can see that at 4 a .m., we are actually at our minimum.
01:09
Then we go up to our maximum at 4 p .m.
01:13
So, let's see here, we need to note that the distance in time between 4 a .m...