The point $\left(9, \frac{\pi}{6}\right)$ can also be represented by which of the following polar coordinates? Select all that apply. A. $\left(9,-\frac{\pi}{6}\right)$ B. $\left(-9, \frac{7 \pi}{6}\right)$ C. $\left(9, \frac{5 \pi}{6}\right)$ D. $\left(-9, \frac{13 \pi}{6}\right)$

Step 1 ：The polar coordinates of a point can be represented in multiple ways. The point \((r, \theta)\) can also be represented as \((-r, \theta + \pi)\) or \((r, \theta + 2\pi)\). This is because adding \(\pi\) to the angle and changing the sign of the radius corresponds to moving to the opposite side of the circle, and adding \(2\pi\) to the angle corresponds to making a full rotation around the circle.

Step 2 ：So, we can represent the point \((9, \frac{\pi}{6})\) as \((-9, \frac{\pi}{6} + \pi)\) or \((9, \frac{\pi}{6} + 2\pi)\).

Step 3 ：Let's calculate these values and see which options they match.

Step 4 ：r = 9

Step 5 ：theta = \pi/6

Step 6 ：new_r1 = -9

Step 7 ：new_theta1 = 7*\pi/6

Step 8 ：new_r2 = 9

Step 9 ：new_theta2 = 13*\pi/6

Step 10 ：The point \((9, \frac{\pi}{6})\) can also be represented as \(\boxed{\left(-9, \frac{7 \pi}{6}\right)}\) and \(\boxed{\left(9, \frac{13 \pi}{6}\right)}\). So, the correct options are B and D.