00:02
For letter a, you're given the point, negative 3, 4, and your angle, theta, has to be between 0 and 4 pi.
00:12
All right, so if we plot negative 3, 1, 2, 3, 4, we are right here, and that would give us, this will be our angle right here.
00:28
So we could find this triangle right here, so this would be negative 3 .3.
00:41
This would be 4, and this would be 5, and here would be our theta measure.
00:49
Well, i'll call that something different.
00:51
That's our reference angle.
00:53
We'll call it alpha.
01:01
And we want to find that.
01:03
So i could say that the sign of alpha is the opposite 4 over the hypotenuse 5, and then i would do inverse sign of 4 -5s to get a degree measure.
01:21
That would give me 53 .13 degrees.
01:28
So you can see that the triangle is in quadrant two.
01:32
So to find that quadrant two angle, which would be this, i would have to subtract that from 180.
01:48
So it will be 1 .26 .87 degrees would be an answer.
01:54
And we can go to 4 pi, so which means i could add another whole rotation onto this so i could go down and around once which is 360 plus then that much more to get my answer so if i add that to 360 i could also have a second answer of 486 .87 degrees and that would also be in that theta range so i have two possible answers for letter a.
02:42
Let's go to letter b.
02:50
We have 5 negative 1, and the theta has to be between 360 and negative 360, but not equal to here.
03:05
So again, let's plot 5 negative 1 would be right here.
03:12
So this would be my reference angle, and i could make a triangle out of that.
03:19
And this is 5, and over here on this side is negative 1.
03:26
And we can consider this my reference angle alpha.
03:33
So i'm going to say the, i don't really need to find the hypotenuse.
03:36
I could do the tangent of alpha is the opposite over the adjacent.
03:42
So to find this angle measurement, i'm going to do inverse tangent of negative 1 5th...