# Rectangular to polar coordinate conversion

• Oct 2nd 2012, 11:58 PM
TWN
Rectangular to polar coordinate conversion
Rectangular coordinates: (0,-6)

Show me how to find the polar coordinates for this please.
• Oct 3rd 2012, 12:18 AM
Prove It
Re: Rectangular to polar coordinate conversion
Well you have not moved across at all, and gone down 6 units. Surely you can read off what the magnitude is. As for the angle, if you started from the positive x axis and went anticlockwise, what angle is swept out?
• Oct 3rd 2012, 12:31 AM
TWN
Re: Rectangular to polar coordinate conversion
Quote:

Originally Posted by Prove It
Well you have not moved across at all, and gone down 6 units. Surely you can read off what the magnitude is. As for the angle, if you started from the positive x axis and went anticlockwise, what angle is swept out?

Here's what is giving me trouble:

tan(theta) = y/x

Therefore, theta = arctan(y/x)

Plugging in x and y, we get

theta = arctan(-6/0)

Negative six over zero is undefined...so now what?
• Oct 3rd 2012, 12:32 AM
Prove It
Re: Rectangular to polar coordinate conversion
Quote:

Originally Posted by TWN
Here's what is giving me trouble:

tan(theta) = y/x

Therefore, theta = arctan(y/x)

Plugging in x and y, we get

theta = arctan(-6/0)

Negative six over zero is undefined...so now what?

Don't apply a formula if you don't understand what it means. Draw a diagram. Surely you can read off your answers from the diagram, if you try it...
• Oct 3rd 2012, 12:38 AM
TWN
Re: Rectangular to polar coordinate conversion
Quote:

Originally Posted by Prove It
Don't apply a formula if you don't understand what it means. Draw a diagram. Surely you can read off your answers from the diagram, if you try it...

Would theta be -pi/2 ? Or -3pi/2 ? Or am I still not looking at it right?
• Oct 3rd 2012, 12:51 AM
Prove It
Re: Rectangular to polar coordinate conversion
It's either \displaystyle \begin{align*} \frac{3\pi}{2} \end{align*} if you move anticlockwise, or \displaystyle \begin{align*} -\frac{\pi}{2} \end{align*} if you move clockwise. Generally we define \displaystyle \begin{align*} \theta \in (-\pi, \pi] \end{align*}, so choose \displaystyle \begin{align*} -\frac{\pi}{2} \end{align*}.

Now what is r?
• Oct 3rd 2012, 01:03 AM
TWN
Re: Rectangular to polar coordinate conversion
Would it be 6 or -6?
• Oct 3rd 2012, 01:34 AM
Prove It
Re: Rectangular to polar coordinate conversion
r represents the magnitude, magnitudes can never be negative.