00:01
In this question, we want to find horizontal and vertical tangents, if there are any, to this pair of parametric functions.
00:08
Now, speaking of tangent, we will need to find the dy, dx.
00:12
We know that the dydx is actually d .y over deter divided by dx over the teter.
00:20
For horizontal tangent, we need to set the dy, dx to zero because it is a flat line like this.
00:33
Then we'll find the theta, sub it into the x and y, you get the coordinates.
00:38
For vertical tangents, it will look like this, a vertical line.
00:45
Everybody knows that a vertical line, the dy, dx is infinity.
00:49
So if your dydx is a fraction, so in this case, u over v, where u and b are functions of teta, we are to set the denominator to zero so that the dydx can be.
01:07
Be infinity.
01:08
So we need to set the denominator to 0.
01:12
So find the titter there.
01:14
Let's start into the x and 1.
01:14
You get a coordinate.
01:16
So let's find our dx teter in dx, deter first.
01:23
So for the x teter, since these two terms are added together, we'll do turn by term, differentiation.
01:30
For the first term, it's a constant number 5.
01:32
When you differentiate, you get 0.
01:34
Second term, 3 is multiplied to cosine teter, so 3 can be left aside.
01:39
Cosine teter, when you differentiate, you'll just get minus sine theta.
01:45
So my dx d theta is just this.
01:50
D .y, the teter, same thing.
01:52
The first term, when we differentiate constant, you'll get zero.
01:56
Second term, sign, titter, when you differentiate, you'll just get cosine teter.
02:01
So, d, y, d, teter is cosine teter.
02:04
So now our d.
02:05
Y, d teter, which is cosine teter, divided by dx d teter.
02:12
Which is just this.
02:16
So for our horizontal tangent, we're going to set the dy, dx to zero.
02:25
Set this whole thing to zero.
02:27
It means what? it means the numerator is equals to zero...