00:01
Tangent alpha equals 12 over 5 and that alpha is between 180 and 270, meaning we're looking at alpha being a third quadrant angle.
00:10
So what we want to know is the sign of alpha over 2, the cosine of alpha over 2, and the tangent of alpha over 2.
00:20
So let's begin by getting our identities.
00:24
So the sign of a half angle, we're going to have this plus or minus, square root of one minus cosine alpha over two.
00:36
So there's going to be our formula where cosine is going to be plus or minus one plus cosine alpha over two, which means we need to know the value of cosine.
00:49
So let's go see what this is going to be.
00:51
So let's draw our angle.
00:52
We're going to have an alpha here.
00:54
Tangent is opposite over adjacent.
00:57
So that'll be 12 and 5.
00:58
But we're dealing with third quadrant, so it's going to be a negative 5 and a negative 12.
01:04
So for cosine, we need to know the hypotenuse.
01:07
I recognize this as a pythagorean triple.
01:10
So that means my hypotenuse is going to be 12 over 13.
01:14
So the cosine of alpha is going to be negative 5 over 13.
01:21
I'm now going to go into my formulas and put that in.
01:24
So we're going to go plus or minus.
01:26
So it's going to be 1 minus negative 5.
01:28
5 over 13 over 2.
01:31
This will be plus or minus doing the same thing...