00:01
All right, in your question, you're asked to find the vertical asthmatotes, if any, of the graph of the function.
00:05
It says use n as an arbitrary integer, if necessary.
00:10
If it doesn't exist, we're going to enter d &e, and our function is f of x equals secant of pi x over 2.
00:17
So ultimately, what we're trying to do is say x equals something, and that value will be the location of a vertical azotot or multiple vertical asmatotes.
00:31
Since we're dealing with the trig function, our answers are more than likely going to be periodic, meaning they were going to repeat.
00:37
So our vertical asthmatode equation is actually going to be a function itself to lay out all the different, because there's going to be an infinite amount of them, vertical asthmatotes.
00:49
What causes vertical asthmatotes? they're caused when we try to divide by zero, and we get an undefined answer.
00:58
So when would secant be dividing by zero? well, that goes back to the relationship with its reciprocal function.
01:09
The reciprocal function of secant is cosine.
01:13
So what i'm interested in here is cosine of what equals zero.
01:20
And i've brought up a unit circle, and you can see the cosine values are your x values.
01:27
And at pi over two, cosine is zero.
01:32
So if we try to take the reciprocal of zero, we get undefined...