What is the polar form of (3, -27)?

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Dustin Durham · Accepted Answer

Step 1To solve 1. we use Pythagoras Theorem      r    =                            3          2                +                              (            -            27            )                    2                          =    3          82      To solve 2. we first find the quadrant that the point lies in.x  is positive while y is negative       ⇒   quadrant IVThen we find the basic angle by taking inverse tangent of             |              y        x            |            α    =                  tan                  -          1                            (                  |                                    -              27                        3                    |                )                  =                  tan                  -          1                            (        9        )            The angle that we are looking for would be      θ    =    -    α        =    -                  tan                  -          1                            (        9        )                  ≈    -    1.460  Therefore, the polar coordinate is             (      3              82            ,      -                        tan                      -            1                                    (          9          )                    )      Note that the answer above is not unique. You can add any integer multiples of       2    π   to       θ   to get other representations of the same point.

What is the polar form of (3, -27)?

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