Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.

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- Apr 16th 2013, 05:07 PMambitionty9Help with Polar Coordinates
Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.

- Apr 16th 2013, 05:42 PMPlatoRe: Help with Polar Coordinates
I would really like to help you, but I cannot deal with the fact you are saddled with a totally outdated system.

Almost all modern mathematics does not recognized "*two pairs of polar coordinates*" as meaningful.

Moreover, we also insist that $\displaystyle =\pi<\theta\le\pi$, nobody uses degrees in mathematics.

Now if you can accept those conventions then $\displaystyle (2,-2)$ has polar form;

$\displaystyle r=2\sqrt{2}$ and $\displaystyle \theta = \arctan \left( {\frac{{ - 2}}{2}} \right) = \frac{{ - \pi }}{4}$.

**You might tell your instructor to get with the modern usage.** - Apr 16th 2013, 06:04 PMSorobanRe: Help with Polar Coordinates
Hello, ambitionty9!

I agree with Plato completely.

However, if weuse this outdated notation . . .*must*

Quote:

Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.

We find that: .$\displaystyle r \:=\:\sqrt{2^2 + (\text{-}2)^2} \:=\:\sqrt{4+4}\:=\:\sqrt{8} \:=\:2\sqrt{2}$

One pair of coordinates is: .$\displaystyle \left(2\sqrt{2},\:315^o\right)$

. . . . . . . . . . .Another is: .$\displaystyle \left(\text{-}2\sqrt{2},\:135^o\right)$