The polar coordinates of point P are given. Find all of its polar coordinates.
-$$\mathrm { P } = ( - 7 , \pi / 5 )$$
A) $( - 7 , \pi / 5 + ( 2 n + 1 ) \pi )$ or $( 7 , \pi / 5 + 2 n \pi )$
B) $( - 7 , \pi / 5 + 2 \mathrm { n } \pi )$ or $( 7 , \pi / 5 + ( 2 \mathrm { n } + 1 ) \pi )$
C) $( - 7 , \pi / 5 + 2 \mathrm { n } \pi )$ or $( - 7 , - \pi / 5 + ( 2 \mathrm { n } + 1 ) \pi )$
D) $( - 7 , \pi / 5 + 2 \mathrm { n } \pi )$ or $( 7 , \pi / 5 + 2 \mathrm { n } \pi )$

Question

Quizplus · Accepted Answer

The polar coordinates $(-7, \theta)$ can be expressed as $(-7, \theta + 2n\pi)$ or $(7, \theta + (2n+1)\pi)$ because adding $2n\pi$ to the angle results in the same direction, and changing the sign of the radius requires adding $\pi$ to the angle.

The Polar Coordinates of Point P Are Given P=(−7,π/5)\mathrm { P } = ( - 7 , \pi / 5 )P=(−7,π/5)

The Polar Coordinates of Point P Are Given $\mathrm { P } = ( - 7 , \pi / 5 )$