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Polar Coordinates

  1. Jul 15, 2012 #1
    Hi,

    I am learning about Polar Coordinates and how they can be written in several equivalent ways.

    I understand how you can add 360 to angles and use negative angles to represent the same point.

    However, I have a very hard time understanding how you can write the same point but with a negative distance r.

    So, the example in the book is r = 10 and θ = 30.

    I really can't see how r = -10 and θ = 210 is equivalent.

    Would anyone mind trying to give me some reasoning better than the one provided by my book?

    Thanks!
     
  2. jcsd
  3. Jul 15, 2012 #2

    eumyang

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    Homework Helper

    (Sorry to nitpick, but you really need the degree symbols. Otherwise, I have to assume that you are in radians.)

    Think of it this way. Let's use the point (8, 135°) as an example. Pretend that you are standing at the origin. θ = 135° means that you would turn and face towards the NW direction. r = 8 indicates that you would walk forward 8 units in the direction of 135°.

    Now (-8, 315°) is an equivalent point. θ = 315° means that you would turn and face towards the SE direction. r = -8 indicates that you would walk backwards 8 units (r is negative), while still facing the SE direction. So you end in the same spot as (8, 135°).
     
  4. Jul 15, 2012 #3
    Firstly, sorry for the degree symbol, I understand. Regarding the explanation, thanks! That is great!
     
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