The polar coordinate can be written as (r, θ) = (r, θ + 2nπ) or
(r, θ) = [ - r, θ + (2n + 1)π ],
where n is any integer.
The polar coordinates point :
P = (r, θ) = (r, - π/6).
Let r be the positive value, then, the polar coordinate can be written as P= (r, - π/6) =
(r, 2nπ - π/6), where n is any integer.
Let r be the negative value, then, the polar coordinate can be written as P = (r, - π/6) =
[ - r, (2n + 1)π - π/6 ],
where n is any integer.
Therefore, all polar coordinates of point P are (r, 2nπ - π/6) and [ - r, (2n + 1)π - π/6 ].
Did you follow?