# Thread: Rectangular to polar coordinate conversion

1. ## Rectangular to polar coordinate conversion

Rectangular coordinates: (0,-6)

Show me how to find the polar coordinates for this please.

2. ## 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?

3. ## Re: Rectangular to polar coordinate conversion

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?

4. ## Re: Rectangular to polar coordinate conversion

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...

5. ## Re: Rectangular to polar coordinate conversion

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?

6. ## 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?

7. ## Re: Rectangular to polar coordinate conversion

Would it be 6 or -6?

8. ## Re: Rectangular to polar coordinate conversion

r represents the magnitude, magnitudes can never be negative.