SOLUTION
To find the additional polar representation of a giving point we use the following
1. By adding or subtracting a multiple of 2π to θ
2. By using a negative radius r, and adding an odd multiple to π
Giving the polar coordinates
[tex](6,\frac{5\pi}{6})[/tex]The additional coordination will be by adding 2π to θ
[tex]\begin{gathered} (6,\frac{5\pi}{6}+2\pi) \\ \\ (6,\frac{17\pi}{6}) \end{gathered}[/tex]Hence one addition coordinate is (6,17π/6)
To find additional polar coordinates,
We subtract 2π from θ
[tex]\begin{gathered} (6,\frac{5\pi}{6}) \\ \text{Then} \\ (6,\frac{5\pi}{6}-2\pi) \\ \\ (6,\frac{5\pi-12\pi}{6})=(6,-\frac{7\pi}{6}) \end{gathered}[/tex]Hence, another additional coordinate is (6,-7π/6 )
Therefore, the two additional polar coordinates are (6,17π/6) and (6,-7π/6 )