00:01
I'm going to do that first problem.
00:02
I'm going to try to do it by hand.
00:05
So what you have is this negative 5, cosine of pi over 12 h plus 12.
00:16
And if the question says, how many hours are there at least 13 customers per hour? what you want to do is say greater than or equal to 13.
00:26
So what i would do at this point is subtract 12 over.
00:31
I mean, you could actually just set this equal to 13.
00:33
But you should get two answers, which is why it's going to be in between whatever the hours are, and then i'll convert it to the minutes or like the time as far as, you know, like 12 and 5 p .m.
00:56
Or something like that.
00:58
Because then your next step would be to divide this negative 5 over.
01:03
And this is the issue, is 1 over negative 5 is not perfect on the unit circle.
01:09
But your next step is to do the inverse cosine on both sides.
01:14
So let me just write that real quick, inverse cosine of negative one -fifth.
01:19
And that cancels out the cosine, so you still have this pi over 12 -h.
01:25
So why do we have two answers? it's because when you do the inverse cosine, and with this being pi over 12, i know that i'm in radian, so make sure you're in radian mode on your calculator.
01:41
So i have to change that real quick.
01:43
Inverse cosine negative one fifth.
01:47
I get an answer of 1 .772.
01:53
A few more decimals, 15, whatever.
01:58
But think about on the unit circle.
02:02
Cosine can be negative in quadrant 2, which is what that is, or quadrant 3.
02:10
Cosine is negative in both of those.
02:12
So what i would do is 2 pi minus that 1 .772...