00:01
So we're trying to find a tangent line for this function secan of x at this x value pi over 6.
00:05
The first thing you want to find is f of pi over 6.
00:08
We're going to need the actual point instead of just the x value.
00:12
And so that would just be secant of pi over 6, which is the same as 1 divided by cosine of pi over 6, and cosine of pi over 6 is equal to the square root of 3 divided by 2.
00:24
So that's going to be equal to 2 divided by the square of 3.
00:26
And if i rationalize the denominator, we're going to get 2 squared 3.
00:30
To 3 divided by 3 as our value for c can of pi over 6.
00:35
And then the next thing we want to do is find our derivative function f prime of x.
00:40
So that's going to be the derivative of 1 divided by cosine of x, but i'm actually going to denote it as cosine of the negative.
00:45
And i won't put it like that since then it kind of looks like a inverse function, but this is just cosine of x to the negative first power.
00:54
And we're taking the derivative of that.
00:56
So we're going to take this negative 1.
00:58
We're going to bring it down.
00:58
We're going to have negative 1 times this...