What is the distance between the following polar coordinates?: ( 5 , 7 π 4 ) , ( 9 , 11 π 8 )

Question

What is the distance between the following polar coordinates?:            (      5      ,                        7          π                4            )        ,          (      9      ,                        11          π                8            )

last99erib · Accepted Answer

Step 1Distance between tow points knowing the polar coordinates is given by the formula using cosine rule      d    =                                        r            1            2                          +                              r            2            2                          -        2                  r          1                          r          2                          cos                      (                          θ              2                        -                          θ              1                        )                                          Given                     r      1        =    5    ,          r      2        =    9    ,          θ      1        =                  (                              7            π                    4                )            c        ,          θ      2        =                  (                              11            π                    8                )            c            d    =                            5          2                +                  9          2                -                  (          2          ⋅          5          ⋅          9          ⋅                      cos                          (                                                11                  π                                8                            -                                                7                  π                                4                            )                                )                                        d              =                  106        -        90                  cos                      (                                          -                3                π                            8                        )                                              ≈        8.4592

What is the distance between the following polar coordinates?: ( 5 , 7 π 4...

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