What is the polar form of ( - 2 , 3 ) ?

Question

What is the polar form of             (      -      2      ,      3      )       ?

Charlize Manning · Accepted Answer

Step 1To solve 1. we use Pythagoras Theorem      r    =                                        (            -            2            )                    2                +                  3          2                          =          13      To solve 2. we first find the quadrant that the point lies in.y is positive while x is negative       ⇒   quadrant IIThen we find the basic angle by taking inverse tangent of             |              y        x            |            α    =                  tan                  -          1                            (                  |                      3                          -              2                                |                )                  =                  tan                  -          1                            (                  3          2                )            The angle that we are looking for would be      θ    =    π    -    α        =    π    -                  tan                  -          1                            (                  3          2                )                  ≈    2.16  Therefore, the polar coordinate is             (              13            ,      π      -                        tan                      -            1                                    (                      3            2                    )                    )      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 <mstyle displaystyle="true"> ( - 2 ,

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