Solve the problem. -$\left( 8 , \frac { \pi } { 6 } \right) , r 0$ and $- 2 \pi

Question

Solve the problem.
-$\left( 8 , \frac { \pi } { 6 } \right) , r > 0$ and $- 2 \pi < \theta < 0$
A) $\left( 8 , - \frac { 11 } { 6 } \pi \right]$
B) $\left( 8 , \frac { 13 } { 6 } \pi \right)$
C) $\left( 8 , - \frac { 5 } { 6 } \pi \right)$
D) $\left( 8 , \frac { 7 } { 6 } \pi \right)$

Quizplus · Accepted Answer

Given the point $\left( 8 , \frac { \pi } { 6 } \right)$ in polar coordinates, where $r > 0$ and $- 2 \pi < \theta < 0$, we need to find the equivalent representation that fits these conditions. The original angle $\frac{\pi}{6}$ is positive, so to find an equivalent angle that is negative and within the given range, we subtract $2\pi$ from it: $\frac{\pi}{6} - 2\pi = \frac{\pi}{6} - \frac{12\pi}{6} = -\frac{11\pi}{6}$. This gives us the point $\left( 8 , - \frac { 11 } { 6 } \pi \right)$, which is within the specified range for $\theta$.

Solve the Problem (8,π6),r>0\left( 8 , \frac { \pi } { 6 } \right) , r > 0(8,6π​),r>0

Solve the Problem $\left( 8 , \frac { \pi } { 6 } \right) , r > 0$