The polar coordinates of point P are given. Find all of its polar coordinates.
-$$\mathrm { P } = \left( 7.2,31 ^ { \circ } \right)$$
A) $\left( 7.2,31 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( - 7.2,31 ^ { \circ } + 360 n ^ { \circ } \right)$
B) $\left( 7.2,31 ^ { \circ } + 180 n ^ { \circ } \right)$ or $\left( - 7.2,31 ^ { \circ } + 180 n ^ { \circ } \right)$
C) $\left( 7.2,31 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( 7.2 , - 31 ^ { \circ } + ( 2 n + 1 ) 180 ^ { \circ } \right)$
D) $\left( 7.2,31 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( - 7.2,31 ^ { \circ } + ( 2 n + 1 ) 180 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

In polar coordinates, a point can be represented in multiple ways. Adding $360^\circ$ to the angle gives a full rotation, resulting in the same direction, so $\left( 7.2,31 ^ { \circ } + 360 n ^ { \circ } \right)$ is correct. Changing the radius to its negative value and adding $180^\circ$ to the angle (or an odd multiple of $180^\circ$) points to the same location, hence $\left( - 7.2,31 ^ { \circ } + ( 2 n + 1 ) 180 ^ { \circ } \right)$ is also correct.

The Polar Coordinates of Point P Are Given P=(7.2,31∘)\mathrm { P } = \left( 7.2,31 ^ { \circ } \right)P=(7.2,31∘)

The Polar Coordinates of Point P Are Given $\mathrm { P } = \left( 7.2,31 ^ { \circ } \right)$