00:01
In this problem, we have been given a function h of t.
00:05
H of t is modeling the number of hours of daylight on day t of the year in fairbanks, alaska.
00:14
We're using a sign function because this is going to be cyclical year after year after year, and we're told that t equals 1 represents january 1st.
00:24
Then we're prompted to find three things.
00:27
We want to find the hours of daylight given the day, and we went to round to the nearest 10th of an hour.
00:35
The first problem we're given is march 21st, the spring equinox, and we're even told that the day is 80.
00:43
It's the 80th day.
00:45
So let's plug this in.
00:46
We're going to find h of 80.
00:49
So we have 12 plus 8 .3 times the sign of 2 pi over 265.
01:00
Sorry, 365, and we're going to plug in 80.
01:07
80 minus 80 gives us zero here.
01:10
So in reality, we're finding the sign of zero.
01:13
We know the sign of zero is zero, so 12 plus 8 .3 times zero gives us 12 plus zero, which is 12 hours.
01:28
The equinox is the day of the year where the day is the same length as the night.
01:36
So if we have 24 hours in a day, we should expect 12 hours of daylight and 12 hours of darkness, which is what we have here.
01:43
So now let's take a look at june 21st, which is the summer solstice.
01:47
This is the longest day of the year...