What is the distance between the following polar coordinates?: ( 10 , 17 π 12 ) , ( 4 , 15 π 8 )

Question

What is the distance between the following polar coordinates?:            (      10      ,                        17          π                12            )        ,          (      4      ,                        15          π                8            )

fongama33 · Accepted Answer

Step 1Polar coordinates of two points are             r      1        =    10    ,          θ      1        =                  17        π            12        =              255      0                    and                    r      2        =    4    ,          θ      2        =                  15        π            8        =          337.5      0      Cartesian coordinate of 1st point is             x      1        =          r      1                                cos          θ                1                   or            x      1        =    10          cos      255        ≈    -    2.588                and                    y      1        =          r      1                                sin          θ                1            =                  y      1        =    10          sin      255        ≈    -    9.659    ∴          (      -      2.588      ,      -      9.659      )      Cartesian coordinate of 2nd point is             x      2        =          r      2                                cos          θ                2                   or            x      2        =    4          cos      337.5        ≈    3.696                and                    y      2        =          r      2                                sin          θ                2            =                  y      2        =    4          sin      337.5        ≈    -    1.53    ∴          (      3.696      ,      -      1.531      )      Distance between two points is      D    =                                        (                          x              1                        −                          x              2                        )                    2                +                              (                          y              1                        −                          y              2                        )                    2                      =        D    =                                        (            -            2.588            −            3.696            )                    2                +                              (            -            9.659            +            1.531            )                    2                      ∴        D    =    10.27   unit

What is the distance between the following polar coordinates?: <mstyle displaystyle="true">

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