Question

If you were to plot all of these polar points, which would not be the same?
a) (2, 15pi/6)

b) (2, pi/6)

c) (-2, -5pi/6)

d) (-2, 7pi/6)

Answer 1

For all of them, |r| = 2, so the length is the same for all.
Perhaps degrees might be easier to visualize for you
(2, 15pi/6) ---> (2,450°) -->(2,90°)
(2, pi/6) ----> (2,30°) , clearly different from the first
(-2, -5pi/6) ---> (-2, -150°) --> (+2,30°) , same as the previous
(-2,210) ----> (+2,30°)

So what do you think?
notice that (r,θ) = (r, 2πk + θ) = (-r, π-θ) , where k is an integer