• drawing vector valued functiions
    6 replies, posted
<cos(t) + tsin(t), sin(t) - tcos(t), t^2> How would you draw something like this without a calculator? Fucking teacher doesnt teach shit. I hope fp is smart enough to help...
Are these 3 separate graphs?
[QUOTE=Harry9397;17645172]Are these 3 separate graphs?[/QUOTE] Could be a 3D parametric graph...but I've never seen one...(i.e. y = cos(t) + tsin(t), x= sin(t) - tcos(t), and z = t^ where t is a function of time).
[QUOTE=Treeh;17645224]Could be a 3D parametric graph...but I've never seen one...(i.e. y = cos(t) + tsin(t), x= sin(t) - tcos(t), and z = t^ where t is a function of time).[/QUOTE] ah, Id never heard of these
[QUOTE=Harry9397;17645279]ah, Id never heard of these[/QUOTE] They're very simple, actually. Rather than having something like y = x^2, you have x = t+ 1 and y = t^2-1 or something like that. You then change t and graph the resulting coordinates. Unlike a "standard" function, parametric functions can have multiple values at a single x coordinate (i.e the vertical line test doesn't need to be satisfied) and because of this, they're often used to represent the position of a particle or some other moving entity.
yes, the parametric equation would be x=cos(t) + tsin(t) y=sin(t) - tcos(t) z=t^2 How are we supposed to graph this by hand??
[QUOTE=mj6969;17646078]yes, the parametric equation would be x=cos(t) + tsin(t) y=sin(t) - tcos(t) z=t^2 How are we supposed to graph this by hand??[/QUOTE] It's difficult, and it's an approximation (i.e. you find a few points at regular intervals...) This applet can do it for you, you can then just copy it down: [url]http://cs.jsu.edu/~leathrum/Mathlets/parapath.html[/url] ...but I can't get it to work. Mathematica can probably do it.
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