What is the polar form of ( - 3 , 14 )

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What is the polar form of             (      -      3      ,      14      )

Carmelo Payne · Accepted Answer

Step 1To solve 1. we use Pythagoras Theorem      r    =                                        (            -            3            )                    2                +                  14          2                          =          205      Step 2To 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                            (                  |                      14                          -              3                                |                )            The angle that we are looking for would be      θ    =    π    -    α        =    π    -                  tan                  -          1                            (                  14          3                )                  ≈    1.78  Therefore, the polar coordinate is             (              205            ,      π      -                        tan                      -            1                                    (                      14            3                    )                    )      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.

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