00:01
The thought process with this is that co -segant is the reciprocal of sign, so it's equal to 1 over sign of x.
00:12
And if you're familiar with the unit circle, like sign is positive.
00:18
So i'm talking about sign right now.
00:19
It's positive in quadrant 1, positive in quadrant 2.
00:23
It doesn't hit negatives until you get to quadrants 3 and 4.
00:28
And we don't repeat the same cycle, the same full cycle, until you get to 2 pi.
00:36
You might even examine the curve, the graph of sign of x that it goes up and then comes back down, and it doesn't actually repeat that curve until you get to 2 pi.
00:48
And then at that point it goes up and back down and does the same thing over here.
00:52
So since the period of sine of x is 2 pi, the period of cosine is also, sorry, the period of cosecine is also 2 pi.
01:02
And then the next question is, where does it have asymptotes? well, if the, the only way to have asymptotes is if you're dividing by zero.
01:11
So you're dividing by zero when sine is equal to zero.
01:16
So that's basically the second question where sign of x equals zero, and that's at every pi 2 pi, 3 pi.
01:27
And what some people will actually do is write out that it's n pi, where n is an integer.
01:36
That's where your asymptotes are located...