00:01
Okay, here i want to find two co -turvinal angles, one plus, one minus for each angle.
00:08
So first step is just draw it.
00:11
So here are the four quadrants.
00:15
And you always measure from the plus x -axis, that's here.
00:20
And if the angle is plus, as it is with 3 pi by 4, you go around counterclockwise.
00:26
So over here then is 3 pi by 4, which means a reference angle down here down here, is pi by four.
00:39
This whole angle here is pi.
00:43
Pi being 180 degrees.
00:46
So right here then really we have three times 45, one three five degrees.
00:51
Now co -terminal angles.
00:55
The first one will be to a plus one first.
00:59
Simply go around a complete circle and end up back over there.
01:06
That one will be three pi by four plus 2 pi and that will be 11 pi by 4 since 2 pi i can write as 8 pi over 4 8 plus 3 11 pi by 4 is co -terminal to 3 pi by 4 of the plus number for minus just go backwards go around clockwise this angle here i'll be pi plus pi by 4 in other words 5 pi by 4 so this angle here is 5 pi by 4 and that's the other one, much than minus 5 pi by 4.
01:56
So minus 5 5 by 4 is your negative co -terminal angle.
02:07
Now over here, this one is the same as saying minus 2 and 1 over 6, 5.
02:18
13 over 6, 2 and 1 6...