00:01
Okay, so to help us solve for this, we're going to actually take an account that if i call, for example, sign of t and i call it u, so that means i'm going to rewrite these in terms of u.
00:16
So 3u squared minus 14u minus 5 equals zero.
00:22
This is now a much simpler quadratic to solve that i don't have to, there's just a lot easier of solving a quadratic that looks like this instead of dealing with sign in there.
00:35
So i do that.
00:37
I'll go ahead and do factoring here.
00:40
So i'm going to get three u and you.
00:44
I'm going to have a be minus five and a plus one because three times a negative five is negative 15 plus one is negative 14.
00:53
So three u plus one equals zero, u minus five equals zero, u equals five, u equals five, and then 3 u equals a negative 1, divide by 3 so that u equals a negative 1 3.
01:05
Well, remember, u is representing sign of t.
01:10
So sign of t equals negative 1 3rd, and the sign of t equals 5.
01:17
So since we're looking at this, let's look at this one first.
01:22
If sign of t ever equals 5, that means we would have a hypothesis that's shorter than the opposite leg.
01:28
So that's actually impossible.
01:30
So we don't have to worry about that one.
01:32
Instead, we just look at sign of t, and when does that equal a negative one -third? okay.
01:40
So we want to find when is sign of t over one -neged of one -third, and i can kind of start off using my, sorry, one second.
01:52
Sorry, so i had to double check.
01:54
So i'll little quick on that one.
01:56
So usually a lot of these problems, you'll have to, once you get to this point, this will be somewhere on the unit circle, but it's not in this case.
02:03
So sign of t is going to negative one -third...