Question

Help please :)
The polar coordinates of a point are unique.
Is this false?

Answer 1

I think it is

Answer 2

It depends on what it means by unique.

Each point in a polar coordinate system is unique, just like all coordinates in a rectangular (\((x,y)\)) coordinate system are unique.

If you pick out any point, there is only one way to describe that point. It has its specific \(r\) and \(\theta\).

Do you use \(r\) and \(\theta\) as your variables?

Answer 3

oh ok yeah I was just given this as a hint to my problem set in my book
Each set of polar coordinates describes a unique point, or location, in the polar coordinate plane.

Answer 4

Right!
So, if you have a point like \((5,\ \pi)\), there are no other coordinates to describe that point.

Answer 5

However a particular point can be described using several coordinate pairs.
that's the continuation

Answer 6

that part is what confused me

Answer 7

A typical way to say this when you prove uniqueness, I think, is to say that

if \((r_1,\ \theta_1)\) are the coordinates that describe a point, and \((r_1,\theta_2)\) describe that point, then \(r_1=r_2\) and \(\theta_1=\theta_2\).

That's what it means to be unique!

Answer 8

Okay! For that, think about
\((5,\ \pi)\)

Now, if you're talking about vectors, you can add two vectors to get a third.

So I think that,
\((2,\ \pi)+(3,\ \pi)=(5,\ \pi)\)

But I'm not sure if we have to go back into rectangular coordinates to see what operations we can allow.

Answer 9

I wonder if
\((1,\ 0)+(1,\ \pi/2)=(\sqrt2,\ \pi/4)\)
is valid notation.



What does it continue to say?

Answer 10

I'll be back in a few hold on

Answer 11

Np!

Answer 12

Which set of polar coordinates describes the same location as the rectangular coordinates 4,-4?

Answer 13

So, you know where \((4,-4)\) is as a rectangular coordinate!

Answer 14

So, how would you find the polar coordinate, \((r,\theta)\)?