00:01
So i think this is kind of a goofy problem because they give you that alpha over two is the angle and that you're in quadrant two.
00:11
But what i'm going to do is just change up this problem and my teacher might not like it.
00:18
But let's just call that theta for a second.
00:21
Because then if i ask you what alpha is equal to in terms of theta, well just you'd have to multiply both sides by two.
00:30
So alpha is equal to 2 theta and it's still in quadrant 2 well i should rephrase that so theta is in quadrant 2 which is important because when i go to look at then that angle that sign of alpha over 2 equals for this so opposite over hypotenuse sign of i'm going to call it theta at this point is equal to forfifis is the opposite over hypotenuse, well, that's going to help me figure out that the adjacent is three because it's a three, four, five, pythagorean triple.
01:15
If you've never heard of a pythagorean triple before, it's always true that three squared plus four squared equals five squared.
01:23
And the reason why that's useful now is we can figure out that cosine would be negative three -fifths.
01:29
So how is that useful for figuring out what sign of alpha is? well, i'm going to call that now sign of 2 theta, and now i can use a double angle formula.
01:40
That's 2 sine of theta, cosine of theta.
01:45
And if you're adamant about following, like the teacher that wrote out sign of alpha, well, that's the same thing as saying 2 sign of alpha over 2 times cosine of alpha over 2.
02:01
But either way, if you follow that formula, i'm just going to write it from right here.
02:07
It's going to be two...