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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: dekoyl on December 10, 2008, 08:41:53 pm

Title: Meaningless parametrics question
Post by: dekoyl on December 10, 2008, 08:41:53 pm: I was simply wondering "what's the point" of parametric equations. From what I see, it's just creating the cartesian form of circles, ellipses and hyperbolae using the knowledge of $sin^{2}(x) + cos^{2}(x) = 1$ .

I'm still on chapter 1 so I'm not sure if it has much significance later.

Sorry for such a stupid question :P Might delete it later to uh.. save space. ::)
Title: Re: Meaningless parametrics question
Post by: Collin Li on December 10, 2008, 08:55:01 pm: No such thing as a stupid question. Essential is stupid for putting it in chapter 1. You use it after differential calculus (first half of the course), in vector calculus.

Here's an example of where parametric equations are applied:

$\textbf{r} = x\textbf{i} + y\textbf{j}$

Now, that's a position vector, and say we want to find the velocity vector. We need to differentiate the position vector with respect to time.

It would help if we had a function $x(t)$ and a function $y(t)$ (parametric equations!)

If we did, we would be able to find: $\textbf{r}(t) = x(t)\textbf{i} + y(t)\textbf{j}$ , and then we could differentiate it with respect to $t$ !

That is the point of them, in VCE.
Title: Re: Meaningless parametrics question
Post by: cobby on December 10, 2008, 09:03:05 pm: Coblin your a genius
Title: Re: Meaningless parametrics question
Post by: dekoyl on December 10, 2008, 09:03:12 pm: Ah thank you so much Coblin ^^

Okay I'll leave this here for those who use Essentials and might be wondering, too.

Quote from: cobby on December 10, 2008, 09:03:05 pm
Coblin your a genius
Is your display name somehow based off "Coblin"? :P
Title: Re: Meaningless parametrics question
Post by: cobby on December 10, 2008, 09:38:06 pm: Quote from: dekoyl on December 10, 2008, 09:03:12 pm
Ah thank you so much Coblin ^^

Okay I'll leave this here for those who use Essentials and might be wondering, too.

Quote from: cobby on December 10, 2008, 09:03:05 pm
Coblin your a genius
Is your display name somehow based off "Coblin"? :P

haha nah its based of my surname :)
but its a pretty cool coincedence :P
Title: Re: Meaningless parametrics question
Post by: NE2000 on December 10, 2008, 10:31:25 pm: It's in chapter one of Quest too. So far to me all their use has been to tell me when it's a semi-ellipse or semi-hyperbola I'm drawing but otherwise yeah in chapter one they don't mean much. But coblin's explanation makes sense :)
Title: Re: Meaningless parametrics question
Post by: Ahmad on December 17, 2008, 08:54:59 pm: Parametric equations offer a more general framework for describing curves (and surfaces!) in two and three dimensions (and beyond). The standard way of describing functions is just a special case of parametric descriptions, since the function y = f(x) can also be described parametrically by $\vec{r} = x \vec{i} + f(x) \vec{j}$ . However there are many curves and surfaces which are described with much greater ease parametrically.

If you're lucky enough to continue with maths at a tertiary level you will see why they're such a powerful tool in multivariable and vector calculus, however in VCE I can understand why you might not see them as such! :)
Title: Re: Meaningless parametrics question
Post by: dcc on December 18, 2008, 01:14:30 pm: Quote from: Ahmad on December 17, 2008, 08:54:59 pm
If you're lucky enough to continue with maths at a tertiary level you will see why they're such a powerful tool in multivariable and vector calculus, however in VCE I can understand why you might not see them as such! :)

As I was reading this thread, I was thinking of exactly the same reply. But you already made it.
Title: Re: Meaningless parametrics question
Post by: humph on December 18, 2008, 01:17:17 pm: Mmmmm tertiary level maths :D

That is all.