Dos anybody know how I do this on a computer? Use a computer to graph the curve with the given vector equation. Make sure you choose a parameter domain and viewpoints that reveal the true nature of the curve.

Question

r(t) = <sin(3t)cos(t),t/4,sin{3t)sin9t)>

Answer 1

There are lots of online graphing sites. But good luck here.
You know that cos(t),t/4,sin(t) is a helix, right? As x and z trace out their circle, the locus moves along the y-axis. But this is an insanely complicated Lissajous figure in the x-z plane, which is also stretched along y as it is traced.

geogebra.com does 3-D parametric curves. Start out with a simple command, like (sin(t),t,cos(t)) to get a feel for using it.