Answer:
All polar coordinates of point P are; (1 , -x/6 + 2nn) and (-1, -x/6 + (2n+1)n)
Explanation:
The polar coordinates can be represented as;
(r,Ф)= (r,Ф+2nn) or (r,Ф) =(-r,Ф+(2n+1)n)
Where n is any integer value.
From the question, we are given that; p=(1,-x/6)
Comparing it with P(r,Ф), then r = 1 and Ф = -x/6
The polar coordinates will now be;
P(r,Ф) = (r,Ф+2nn) = (1 , -x/6 + 2nn)
Where; n is any positive integer and the value of r is positive.
While;
P(r,Ф) =(-r,Ф+(2n+1)n) = (-1, -x/6+(2n+1)n) and n is any positive integer and the value of r is negative.
Thus, all polar coordinates of point P are (1 , -x/6 + 2nn) and (-1, -x/6 + (2n+1)n)