Question

Which of the following pairs of coordinates represents the same point in polar coordinates? Check all that apply.

A. (r, theta) and (r, theta + pi)
B. (r, theta) and (-r, theta + 2pi)
C. (r, theta) and (r, theta + 2pi)
D. (r, theta) and (-r, theta)

Answer 1

I am not too familiar with these but I think, if I remember correctly, that the answers would be A and C?

Answer 2

Yep A and C *gives medal*

Answer 3

To find the equivalent polar coordinates

\((r, \theta) = (r, ~ \theta \pm 2n\pi)\)

or

\((r, \theta) = (-r, ~\theta \pm (2n+1)\pi)\)


A simpler way to see this would be when n = 1

\((r, \theta) = (r, ~ \theta + 2\pi)\)
\((r, \theta) = (-r, ~\theta + \pi)\)

Trying to explain how this works would result in me writing a massive wall of text which would just be difficult to understand. This short video should help you visualize and understand it clearly.
https://www.youtube.com/watch?v=-P_2tXNqwZQ

Answer 4

One last thing I would like to add is that answer choice A is only correct if the "-" was omitted accidentally as it should read (-r, theta + pi)