What is the polar form of ( - 3 , 4 ) ?

Question

What is the polar form of             (      -      3      ,      4      )       ?

Madden Luna · Accepted Answer

Step 1If             (      a      ,      b      )       is a are the coordinates of a point in Cartesian Plane, u is its magnitude and       α   is its angle then             (      a      ,      b      )       in Polar Form is written as             (      u      ,      α      )       .Magnitude of a cartesian coordinates             (      a      ,      b      )       is given by                               a          2                +                  b          2                     and its angle is given by                     tan                  -          1                            (                  b          a                )            Let r be the magnitude of             (      -      3      ,      4      )       and       θ   be its angleMagnitude of             (      -      3      ,      4      )        =                                        (            -            3            )                    2                +                  4          2                      =                  9        +        16              =          25        =    5    =    r  Angle of             (      -      3      ,      4      )        =                  tan                  -          1                            (                  4                      -            3                          )              =                  tan                  -          1                            (        -                  4          3                )              =    -          53.13      0            ⇒   Angle of             (      -      3      ,      4      )        =    -          53.13      0      But the given point (-3,4) is in second quadrant so we have to add             180      0       in the angle.      ⇒   Angle of             (      -      3      ,      4      )        =    -          53.13      0        +          180      0        =          126.87      0        =    θ        ⇒          (      -      3      ,      4      )        =          (      r      ,      θ      )        =          (      5      ,              126.87        0            )            ⇒          (      -      3      ,      4      )        =          (      5      ,              126.87        0            )      Note that the angle is given in degree measure.

What is the polar form of <mstyle displaystyle="true"> ( - 3 ,

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