00:01
So we have the function big t of little t.
00:04
30 plus 18 sine.
00:08
Of pie t over 12.
00:12
What do we got the temperature at 9 am now 9 am? is corresponding to t equals zero.
00:21
So big t of zero.
00:23
Well, if we plugged in zero here, sine of zero is zero, so you're looking at 30 plus 18 times zero.
00:32
What should give me 30? i don't know if you have to give the units, but it did say degrees fahrenheit.
00:39
But then they ask next for big t of 3 pm.
00:45
So you do have to think a little bit that 3 pm is six hours later.
00:50
Like 12 pm is three hours later.
00:55
And so 3 pm is three hours after 12 pm.
00:58
So t equals six.
01:00
So now you have to think about six over 12 is pi over two and sine of pi over two equals one.
01:10
And we're looking at 48 degrees fahrenheit.
01:14
And i, again, i don't know if you need the units.
01:17
So i'll just circle the 48.
01:18
Now, if you're supposed to do calculus on this next one from 9 am to 9 pm, then we have 12 hours.
01:28
So it's one over 12 minus zero, the integral going from zero to 12 of that function.
01:44
You put some brackets in there because now you have 30 t.
01:50
The integral of sine is actually negative cosine...