Question

Find all polar coordinates of point P where P = ordered pair (5 , pi/3).

Answer 1

hi :DD

Answer 2

the radial lenghth is five and the angle from the x axis is pi/3..is'nt this already in polar co ordinates?

Answer 3

so, obviously, the ordered pair (5, pi/3) works, since that is P. But if you go another 2pi around, you have the ordered pair (5, 7pi/3) which is the same point.

in fact, if you find the ordered pair
\[(5, (2\pi n)+\pi/3)\] for any integer n, it gets you to the same point

Answer 4

but there's one more thing to consider...

Answer 5

the point (-5, -2pi/3) also works...as seen in the diagram below

Answer 6

so, the points \[(-5, (2\pi n)-2\pi/3)\] also work.

Answer 7

(5, pi divided by 3 + nπ) or (-5, pi divided by 3 + nπ)

(5, pi divided by 3 + (2n + 1)π) or (-5, pi divided by 3 + 2nπ)

(5, pi divided by 3 + 2nπ) or (-5, pi divided by 3 + (2n + 1)π)

(5, pi divided by 3 + 2nπ) or (-5, pi divided by 3 + 2nπ)

Answer 8

Those are my options

Answer 9

so based on my first set, you can narrow it down to one of the last two, right?

Answer 10

Yes

Answer 11

so of those 2, which seems more likely? if you don't know, it's ok, i just want to see if you can reason it out....

Answer 12

Last one?

Answer 13

so let's consider tha last one...specifically, the second set of the last one, (-5, pi/3 + 2npi)

look at the circle i drew and imagine you are standing on the center...

you turn so that you are facing pi/3. Now, you walk backwards 5 (walk along the line until you hit the circle...where would you be?