The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$
- $( 4 , - 4 )$

Question

The rectangular coordinates of a point are given. Express the point in polar coordinates with $$r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$$
-$( 4 , - 4 )$
A) $\left( 4 \sqrt { 2 } , 315 ^ { \circ } \right)$
B) $\left( 4 \sqrt { 2 } , 225 ^ { \circ } \right)$
C) $\left( 4 \sqrt { 2 } , 45 ^ { \circ } \right)$
D) $\left( 4 \sqrt { 2 } , 135 ^ { \circ } \right)$

Quizplus · Accepted Answer

The polar coordinates are found using $ r = \sqrt{x^2 + y^2} $ and $ \theta = \tan^{-1}(y/x) $. For $(4, -4)$, $ r = \sqrt{4^2 + (-4)^2} = 4\sqrt{2} $ and $ \theta = \tan^{-1}(-4/4) = \tan^{-1}(-1) = 315^\circ $.

The Rectangular Coordinates of a Point Are Given r≥0 and 0∘≤θ<360∘. r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }r≥0 and 0∘≤θ<360∘.

The Rectangular Coordinates of a Point Are Given $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$