Parameterization of the negative half of the y-axis

Question

I need to parameterize the negative half of the y-axis in spherical and cylindrical coordinates. I know what spherical and cylindrical coordinates are, just not sure where to start to parameterize the negative half of the y-axis

Answer 1

You've probably got some equations that look something like this:
$x = r\cos(\phi),$
$y = r\sin(\phi),$
$z = z,$
but your class may use different names than I did.

For the negative y-axis, you want x=0, z=0, and y negative.

Answer 2

Easily done:

$$\begin{align*}x&=0\\y&=-|t|\\z&=0\end{align*}$$

I leave the justification to you...