The rectangular coordinates of a point are given. Express the point in polar coordinates with $\mathrm { r } \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ }$
- $( 3,3 )$

Question

The rectangular coordinates of a point are given. Express the point in polar coordinates with $$\mathrm { r } \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( 3,3 )$
A) $\left( 3,90 ^ { \circ } \right)$
B) $\left( 3 \sqrt { 2 } , 45 ^ { \circ } \right)$
C) $\left( 3 \sqrt { 2 } , 135 ^ { \circ } \right)$
D) $\left( 3,45 ^ { \circ } \right)$

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 $(3,3)$, $r = \sqrt{3^2 + 3^2} = 3\sqrt{2}$ and $\theta = \tan^{-1}\left(\frac{3}{3}\right) = 45^\circ$, making the correct answer $\left(3\sqrt{2}, 45^\circ\right)$.

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

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