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

Question

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

anonymous · Answer

I was able to determine by using the formula r^2=x^2+y^2
r=2 times the square root of 2

anonymous · Answer

Also by using the formula tan theta=y/x
Then theta=(-pi/4)+npi

anonymous · Answer

For my first comment its actually r=plus/minus 2 times the square root of 2

ganeshie8 · Answer

looks good^

ganeshie8 · Answer

All the representations :

$\large \left( 2\sqrt{2},  ~~\frac{-\pi}{4} + 2n\pi\right)$

and

$\large \left( -2\sqrt{2},  ~~\frac{-\pi}{4}+\pi  + 2n\pi\right)$

anonymous · Answer

Which one of these would be the answer then?
 
(2 square root of 2, 135°), (-2 square root of 2, 315°) 

 (2 square root of 2, 315°), (-2 square root of 2, 135°)

ganeshie8 · Answer

plugin n=1 in first solution
plugin  n=0 in second solution

anonymous · Answer

so it would be the second on then

ganeshie8 · Answer

$\large \left( 2\sqrt{2},  ~~\frac{-\pi}{4} + 2\pi\right)$

and

$\large \left( -2\sqrt{2},  ~~\frac{-\pi}{4}+\pi  +0\right)$

anonymous · Answer

(2 square root of 2, 315°), (-2 square root of 2, 135°)

ganeshie8 · Answer

Yep !