Find all polar coordinates of point P where P = (1,pi/3)
(1, pi divided by 3 + 2nπ) or (-1, pi divided by 3 + (2n + 1)π)

(1, pi divided by 3 + (2n + 1)π) or (-1, pi divided by 3 + 2nπ)

(1, pi divided by 3 + nπ) or (-1, pi divided by 3+ nπ)

(1, pi divided by 3 + 2nπ) or (-1, pi divided by 3 + 2nπ)

Question

Find all polar coordinates of point P where P = (1,pi/3)
(1, pi divided by 3 + 2nπ) or (-1, pi divided by 3 + (2n + 1)π)

 (1, pi divided by 3 + (2n + 1)π) or (-1, pi divided by 3 + 2nπ)

 (1, pi divided by 3 + nπ) or (-1, pi divided by 3+ nπ)

 (1, pi divided by 3 + 2nπ) or (-1, pi divided by 3 + 2nπ)

psymon · Answer

Well, clearly we can have the original and have it repeat every 2pi, so (1, pi/3 + 2npi) is correct. Now the all the other options force us to look at pi/3 and go backwards:

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psymon · Answer

So we gotta get from -1 to positive 1. Well, I can just add pi to go around to the other side of the circle. Problem with that is I can't add npi because then I will only be at the correct spot when n is odd. So that means the only possible answer is (2n+1)pi. Because no matter what n is, I will always have an odd multiple of pi, which is what I need to get back to the correct location.