Solve the problem.
-$\left( 9 , \frac { \pi } { 3 } \right) , \mathrm { r }

Question

Solve the problem.
-$\left( 9 , \frac { \pi } { 3 } \right) , \mathrm { r } < 0$ and $2 \pi < \theta < 4 \pi$
A) $\left( - 9 , \frac { 10 } { 3 } \pi \right)$
B) $\left( - 9 , - \frac { 8 } { 3 } \pi \right)$
C) $\left( - 9 , \frac { 7 } { 3 } \pi \right)$
D) $\left( - 9 , \frac { 4 } { 3 } \pi \right)$ Select the representation that does not change the location of the given point.

Quizplus · Accepted Answer

Given a point in polar coordinates $(r, \theta) = \left( 9, \frac{\pi}{3} \right)$ with $r < 0$ and $2\pi < \theta < 4\pi$, to maintain the same location while meeting the conditions, we adjust $\theta$ by adding $2\pi$ to move it into the specified range, resulting in $\theta = \frac{\pi}{3} + 2\pi = \frac{7\pi}{3}$, and $r$ becomes $-9$ to satisfy $r < 0$. Thus, the correct representation is $\left( -9, \frac{7\pi}{3} \right)$.

Solve the Problem (9,π3),r<0\left( 9 , \frac { \pi } { 3 } \right) , \mathrm { r } < 0(9,3π​),r<0

Solve the Problem $\left( 9 , \frac { \pi } { 3 } \right) , \mathrm { r } < 0$