Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.
I would really like to help you, but I cannot deal with the fact you are saddled with a totally outdated system.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.
Hello, ambitionty9!
I agree with Plato completely.
However, if we must use this outdated notation . . .
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: .$\displaystyle \left(\text{-}2\sqrt{2},\:135^o\right)$