# Homework Help: Help describing a region in polar coordinates

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1. Apr 21, 2017

### BillyC

1. The problem statement, all variables and given/known data
If (r, θ) are the polar coordinates of a point then describe the region defined by the restrictions
-1 < r < 0, π/2 < θ < 3π/2

2. Relevant equations
No clue

3. The attempt at a solution
I tried drawing the curve in a polar grid by starting at π/2 and finishing at 3π/2. I was careful to draw it according to the negative values of r. I ended up getting a shape that looked like half of a heart. So my answer was that it was a cardioid.

2. Apr 22, 2017

### BvU

Hi,

Very unusual definition of polar coordinates (negative distance ? )
Strange. Can you post it ?

3. Apr 22, 2017

### Staff: Mentor

The r coordinate can be negative. For example, $(2, 5\pi/4)$ and $(-2, \pi/4)$ identify the same location.

No, that isn't right. The shape you get should be half a circular disk.

@Nidum, in answer to the question you posted, but deleted, yes, that is what is meant.

4. Apr 22, 2017

### Nidum

Here it is again :

I think though that using ( r , theta + pi ) would be preferable to using ( - r , theta ) for the coordinates . It's difficult to visualise what - r means in polar coordinates .

5. Apr 22, 2017

### Nidum

6. Apr 22, 2017

### Staff: Mentor

It's really not that difficult to visualize. The ray in the first quadrant has r > 0. For a negative r with theta being the same, just go out the opposite direction as r is in. This works the same way as it does for vectors, where u and -u point in opposite directions.

7. Apr 22, 2017

### Buffu

With that negative $r$, I don't how you will plot the curve easily since most graphing calculator assume r to be positive.

Also it is impossible to get -ve $r$ from cartesian coordinates since $\sqrt{x^2 + y^2}= r$.

8. Apr 22, 2017

### Nidum

No calculator needed . In fact no calculation needed .

Once you work out what is actually meant by the problem statement you can draw the required shape using simple straight lines and arcs .

Last edited: Apr 23, 2017
9. Apr 22, 2017

### Staff: Mentor

But if the relationship is instead $r^2 = x^2 + y^2$, then you can get negative values of r.

From wikipedia, https://en.wikipedia.org/wiki/Polar_coordinate_system: