Answer
See images:
Work Step by Step
We are given a parametric curve:
$r(t) $
In geogebra:
Curve$( \sin(t), \sin(2t), \cos(4t), t, 0, 2\pi)$
We project onto the three coordinate planes:
$xy$ plane $(z=0)$
$r(t)= <\sin \sin>$
In geogebra:
Curve$( \sin(t), \sin(2t), 0, t, 0, 2\pi)$
$xz$ plane $(y=0)$
$r(t)= <\sin \cos>$
In geogebra:
Curve$( \sin(t), 0, \cos(4t), t, 0, 2\pi)$
$yz$ plane $(x=0)$
$r(t)= <0,\space \sin(2t),\space \cos (4t)>$
In geogebra:
Curve$( 0, \sin(2t), \cos(4t), t, 0, 2\pi)<\sin><\sin>$
