Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$
- $( 0 , \sqrt { 5 } )$

Question

Determine two pairs of polar coordinates for the point with $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( 0 , \sqrt { 5 } )$
A) $\left( 5,90 ^ { \circ } \right) , \left( - 5,270 ^ { \circ } \right)$
B) $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 270 ^ { \circ } \right)$
C) $\left( \sqrt { 5 } , 270 ^ { \circ } \right) , \left( - \sqrt { 5 } , 90 ^ { \circ } \right)$
D) $\left( 5,0 ^ { \circ } \right) , \left( - 5,180 ^ { \circ } \right)$

Quizplus · Accepted Answer

The point $(0, \sqrt{5})$ in Cartesian coordinates is directly above the origin, at a distance of $\sqrt{5}$ units. In polar coordinates, this corresponds to a radius of $\sqrt{5}$ and an angle of $90^\circ$ for the positive radius. For the negative radius, the point can be represented as having a radius of $-\sqrt{5}$ and an angle of $270^\circ$, which effectively points in the same direction but is measured in the opposite sense.

Determine Two Pairs of Polar Coordinates for the Point With 0