answered
2014-06-30 13:31:28 -0600
The way I see it, you have a few options. The first (and probably easiest, yet most inflexible) is to use WolframAlpha. You can type something like:
parametric plot (sin t, cos t, cos(8t))
And it will graph it for you. Unfortunately, there is no interactivity, and that's not cool at all—let alone groovy! Your second option is to use Mathematica. If you download it from the class site link, you can input your UNCA email address and get it for free. This is a reference guide on how to use the ParametricPlot3D
function. All you have to do is type something like this:
ParametricPlot3D[{Sin[u], Cos[u], u}, {u, 0, 10}]
More generally, the function works like this:
ParametricPlot3D[{fx, fy, fz}, {u, umin, umax}]
Where fx
is the $x$ component of your curve, fy
is the $y$ component of your curve, and fz
is the $z$ component of your curve. The second parameter, {u, umin, umax}
, is also made up of three parts. The first part, u
tells Mathematica what variable you want it to use for the calculations (like $t$ or $x$ or $u$). The second and third parameters let Mathematica determine the lower and upper values for your function, and restricts the domain.
Your third option is Mac-only. If you go into Utilities in your Application folder, you will find an app called "Grapher". It's a very nice piece of software! When you open it, select "3D Graph" then "Default". Next, in the bottom left corner of the window that appears, click the "+" then "New Equation From Template...". Choose "Cartesian Surface" and you should be good to go!