We just converted this into a parametric equation or a set of parametric equations.

You might say well what's the difference between this parametric equation and this parametric equation?

These two things are parametric equations.

So both of these parametric equations, both sets of parametric equations have the exact same path.

That's just a standard way of describing a parametric equation or curve using 2 parametric equations.

And that's why parametric equations are useful.

learn a little bit about parametric equations.

And that's why you need these parametric equations.

You don't have to have a parametric equation.

So if you watch the videos on parametric equations, this is just a traditional parametric definition of this line right there.

But this is about parametric equations and not trigonometry.

And just like that, we have three parametric equations.

Because there's no way, just with the information that you're given here, to know that you should go to this parametric equation or this parametric equation or any of an infinite number of parametric equations.

You can turn into an arbitrary number of parametric equations.

So the whole curve described by this parametric equation will

So what you see is that this set of parametric equations has the exact same shape of its path as this set of parametric equations.

So the direction of t's parametric equations is in that direction.

But our goal isn't here just to graph a parametric equation.

So there's all sorts of parametric equations that you can define.

So because it's a parametric equation, we can draw some arrows.

So instead of writing x times y, let's substitute the parametric form.

But this parametric equation actually doesn't just describe this part of the curve.

And time tends to be the parameter when people talk about parametric equations.

When I just look at that, unless you deal with parametric equations, or maybe polar coordinates a lot, it's not obvious that this is the parametric equation for an ellipse.

We can even set up a parametric equation that goes in the other direction.

And let's say that you were asked to turn this into a parametric equation.

As you probably realize, that this is a video on parametric equations, not physics.

The intention is to give you the motivation behind why parametric equations even exist.

If these parametric equations really are describing some type of motion, it would be counterclockwise.

Watch the parametric functions videos if you want a little bit more depth on that.

All sorts of interesting problems come out of using parametric equations, not just in physics.

So if you have the shape, you don't know what parametric equation you can go back to.

And just to kind of hit the point home of kind of making up a parametric equation.

But what was interesting, by making it a parametric equation, we know the direction of the car.

So in our first situation So they both We established that both this set of parametric equations and this set of parametric equations, they both have the same overall, I guess we could say, shape of their path.