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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

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2 Answers 2

up vote 0 down vote accepted

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.

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Easily done:

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

I leave the justification to you...

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Yep, this is what I was thinking, just wasn't too sure if the negative abs value would get it for me. Thanks! –  William Carey Nov 15 '11 at 2:06
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