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

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 $\boxed{{\displaystyle (-9,\frac{7\pi }{6})}}$ and $\boxed{{\displaystyle (9,\frac{13\pi }{6})}}$. So, the correct options are B and D.