Question

polar coordinates

Answer 1

Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.

Answer 2

Is there anything that you know that can help?

Answer 3

i get polar coordinates, and i know greater than and equal to but ive never seen them combined before... plus it has theta in the middle and not x.. .-. so idk

Answer 4

Okay! So, combining them like that is very common. What it means when you write
0° ≤ θ < 360°
is that the angle, \(\theta\), is between 0 and 360 degrees, including zero.

Answer 5

See, you can break it up into
0° ≤ θ
(the angle is greater than zero or is zero)
(and)
θ < 360°
(the angle is less than 360 degrees)

So, combining them,
the angle is greater than zero or is zero
and
the angle is less than 360 degrees

So, the angle is between 0 and 360, including 0.

Answer 6

The allowed angles are

Answer 7

Does that sound okay to you?

Answer 8

yeaj, i already get graterthan and lessthan. plus i figured, since it only goes up to 360 it would only be able to go in a circle once because alot of these angles go over .-. which is really annoying...

Answer 9

Right. So you can't use something like \(0^\circ\) and \(360^\circ\) to get to the same point. And you can't use \(1^\circ\) and \(361^\circ\) to get to the same point either. No negatives either.

So, \(\theta\) alone can't help us.

But what about \(r\)?
What if \(r\) was negative?

Answer 10

First, let's look at the point \((5,-5)\), and make it polar.

Answer 11

wait r as in the radius?

Answer 12

Yep!

Answer 13

oh okay so find the distance from 0.0 to 5,-5 right?

Answer 14

Right, that is \(r\) for one polar point! Now, what is the \(\theta\) that goes with it, to make that polar point?

Answer 15

Oh, sorry, got ahead of myself. That is \(r\), so I guess we should find a number for it.

Answer 16

Can you do that?

Answer 17

x^2 + y^2 = r^2
(5)^2 + (-5)^2 = r^2
25 + 25 = r^2
50 = r^2
sqrt50 = r
5sqrt2 = r.

Answer 18

Great!
So \(5\sqrt2\) is the \(r\) value for one polar point. What is the \(\theta\) for it?

Answer 19

um holdon ima go look up the circle chart thingy

Answer 20

Let me know if you need a hand with that at all.
Okay!

Answer 21

If you want to work through it, we can. It might get you on the track to memorizing it if you want. But it is a lot of discussion, and might be distracting. Up to you!

Answer 22

wouldnt it be arctan of -1?
cuz
y/x = sin theta / cos theta
y/x = tan theta
-5/5 = tan theta
-1 = tan theta
theta = arctan (-1).