Thread: Find polar coordinates

Hey I am not sure how to find the second coordinate of these polar coordinates.

a) Find polar coordinates (r, θ) of the point (4, -4), where r > 0 and 0 ≤ θ ≤ 2π.

So



I tried doing
θ=
θ=
θ=
θ=

But this is incorrect?

For r < 0 and 0 ≤ θ ≤ 2π.



How do I find theta?

Originally Posted by mmattson07

Hey I am not sure how to find the second coordinate of these polar coordinates.

a) Find polar coordinates (r, θ) of the point (4, -4), where r > 0 and 0 ≤ θ ≤ 2π.

So



I tried doing
θ=
θ=
θ=
θ=

But this is incorrect?

For r < 0 and 0 ≤ θ ≤ 2π.



How do I find theta?

Your calculation of is correct.

To find , first note that the point is in the fourth quadrant. So you would need to find the focus angle, i.e. for the point , and then subtract it from .
So







.

I see. So how would that differ for r<0?

Can you ever possibly have a negative radius?

Perhaps not. I just added pi to account for -r.

represents the distance between a point and the origin.

A distance, in other words, a length, can never be negative.


I don't see why you would add .

Originally Posted by mmattson07

Hey I am not sure how to find the second coordinate of these polar coordinates.

a) Find polar coordinates (r, θ) of the point (4, -4), where r > 0 and 0 ≤ θ ≤ 2π.

So



I tried doing
θ=
θ=
θ=
θ=

But this is incorrect?

That's incorrect only because you specifically said " " and is less than 0. Since a complete circle is , adding , gives you exactly the same point and is now in the correct interval: is larger than 0 and less than .

For r < 0 and 0 ≤ θ ≤ 2π.



How do I find theta?