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) $\left( 4 \sqrt { 2 } , 135 ^ { \circ } \right)$
B) $\left( 4,90 ^ { \circ } \right)$
C) $\left( 4 \sqrt { 2 } , 45 ^ { \circ } \right)$
D) $\left( 4,45 ^ { \circ } \right)$

Quizplus · Accepted Answer

To convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, \theta)$, use the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. For the point $(4, 4)$, $r = \sqrt{4^2 + 4^2} = \sqrt{32} = 4\sqrt{2}$, and $\theta = \tan^{-1}\left(\frac{4}{4}\right) = \tan^{-1}(1) = 45^\circ$.

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 $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$