The polar coordinates of point P are given. Find all of its polar coordinates.
-$$\mathrm { P } = \left( 8 , - 22 ^ { \circ } \right)$$
A) $\left( 8 , - 22 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( - 8 , - 22 ^ { \circ } + 360 n ^ { \circ } \right)$
B) $\left( 8 , - 22 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( - 8 , - 22 ^ { \circ } + ( 2 n + 1 ) 180 ^ { \circ } \right)$
C) $\left( 8 , - 22 ^ { \circ } + 180 n ^ { \circ } \right)$ or $\left( 8,22 ^ { \circ } + 180 n ^ { \circ } \right)$
D) $\left( 8 , - 22 ^ { \circ } + 360 n ^ { \circ } \right)$ or $\left( 8,22 ^ { \circ } + ( 2 n + 1 ) 180 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

In polar coordinates, a point can be represented in multiple forms. The angle can be adjusted by adding $360^\circ$ (or $2\pi$ radians) any number of times ($n$), as this brings the point full circle back to its original position. Additionally, the radius can be negative, which effectively flips the point across the origin, changing its angle by $180^\circ$. This is represented by adding $(2n+1)180^\circ$ to the angle when the radius is negative. Therefore, option B correctly represents all possible polar coordinates for point P.

The Polar Coordinates of Point P Are Given P=(8,−22∘)\mathrm { P } = \left( 8 , - 22 ^ { \circ } \right)P=(8,−22∘)

The Polar Coordinates of Point P Are Given $\mathrm { P } = \left( 8 , - 22 ^ { \circ } \right)$