00:02
Okay, i want to find the reference angle for these angles right here, a, b, c, and d.
00:11
The reference angle is the smallest angle from the terminal side to the x axis.
00:23
I'm assuming everything is in radians, unless it said it was in degrees, like part d said it was 5 .1 degrees.
00:32
Most of these are not in terms of pi.
00:36
Let's get some reference angles on here, like starting with 0 radians or 0 degrees.
00:47
Then up here is going to be the positive y axis is going to be pi over 2 radians.
00:57
What is that as a decimal? that is about 1 .57.
01:03
Any number between 0 and 1 .57 will be in that first quadrant.
01:13
Then over here we've got pi radians, which is about 3 .14.
01:20
Then over here we've got 3 pi over 2 radians.
01:25
I can take pi and multiply it by 3 over 2, and that's about 4 .71 radians.
01:32
Then i come back to the positive x axis, and now i'm at 2 pi or 6 .28 radians.
01:49
Part a is 0 .9, so we can sketch that on here.
02:00
I'll use blue.
02:01
Here's my initial side, the terminal side.
02:04
It's not going to go past pi over 2 because pi over 2 is only 1 .57.
02:09
It's going to be something like that, 0 .9 radians.
02:16
We can see it's in the first quadrant, so that reference angle is going to be the same as our angle, which was 0 .9.
02:32
0 .9 pi, well we know 1 pi is over here on the left, on the negative x axis.
02:43
It's not quite to 1 pi.
02:50
It's 9 tenths pi.
02:53
Maybe it would be about there, probably a little bit further.
02:57
So that's 0 .9 pi, and we can see the closest angle to the x axis is here.
03:11
So that's going to be just a little bit short of pi...