00:01
So in this problem, you're being asked to find a reference angle for each of the following.
00:03
So remember, a reference angle is an acute angle, meaning between 0 and 90, that is created in the reference triangle that is drawn towards your x -axis for the given angle.
00:14
So the first thing we want to do is draw the given angle.
00:17
So remember, this is 0 degrees, and we always go counterclockwise for positive angles.
00:22
So if we were to draw, 198 degrees, this would be 90, 180, so if we go a little bit further, we would get to a hundred ninety eight degrees.
00:32
So this angle right here is one hundred ninety eight degrees.
00:35
Well if we were to draw the reference triangle, remember always goes to the x -axis.
00:40
So our reference angle would be this angle right here.
00:43
Well remember from here to here was 180.
00:47
So that means how much further would we have to go to get to 198? so to find it we would simply take 198 and subtract 180 which would be equal to 18 degrees.
00:58
So that would be the reference angle.
01:00
Okay, now let's take a look at part b.
01:02
In part b, we are given an angle that is negative 78 degrees.
01:07
Well, again, the easiest way to do this is to jar.
01:10
So negative 78 degrees.
01:13
Well, because it's negative, we're going to go clockwise.
01:15
And because it's less than 90, we're not going to go that full all the way down to our y -axis.
01:21
So this is going to be an angle in the 4th quadrant.
01:23
So this angle right here would be 78 degrees.
01:25
So if i was to make my reference triangle, my reference angle would actually still be this angle right here, which is 78.
01:33
The only difference is it's going to be positive.
01:35
So the reference angle in this case is, in fact, 78 degrees.
01:40
All right, let's take a look at c.
01:42
For part c, we have 143 degrees.
01:46
So again, easiest way to do this is to jar.
01:49
So because it's positive, we're going to go counterclockwise.
01:52
So this would be 90.
01:53
But 143 is less than 180.
01:55
So it's going to be somewhere here in the second quadrant.
01:58
So this is 143 degrees.
02:01
So if we made our reference triangle, our reference angle would be this angle right here.
02:05
So what we would do to find our reference triangle angle is we would take 180 degrees and subtract the 143 to get this remaining angle.
02:13
Well, 180 minus 143 is equal to 37.
02:18
So 37 degrees will be the reference angle.
02:22
All right.
02:22
Let's scroll down a little bit here...