00:01
In this question, we are asked to find the angle between 0 and 2 pi, a terminal with 19 pi over 6.
00:07
And the first step would be to rewrite 19 pi over 6 as 12 power 6 plus 7 piver 6.
00:21
This becomes 12 pi over 6 plus 7 power 6, and then 12 pi or 6 could be simplified to 2 pi, and there is 7 pi 4x remaining.
00:38
Now, what we are going to do next, so 19 pi over 6 could be written as 2 pi plus 7 pi over 6.
00:47
Now recall that 2 pi corresponds to one complete revolution around the origin starting from the positive x axis.
00:57
And then there is a part which corresponds to 7 pi over 6.
01:03
Note that 7 pi over 6 now 7 pi over 6 equals to 6 plus pi over 6 plus pi over 6 plus 5 over 6.
01:17
This equals to pi plus pi over 6.
01:23
And pi is half, since two pi is one full revolution, pi corresponds to half over evolution.
01:34
And then there is a part corresponding to pi over 6...