What is the distance between the following polar coordinates?: ( 6 , 17 π 12 ) , ( 5 , 9 π 8 )

Question

What is the distance between the following polar coordinates?:            (      6      ,                        17          π                12            )        ,          (      5      ,                        9          π                8            )

Harley Fitzpatrick · Accepted Answer

Step 1Polar coordinates are written in the following format:             (      r      ,      θ      )      Where r is the distance from the origin and       θ   is the angle rotated counterclockwise about the origin from the x-axis. You can convert to polar coordinates by using the following formulas.      x    =    r          cos              (        θ        )                  y    =    r          sin              (        θ        )                        tan              (        θ        )              =                  y                    x            If you plot your points in either Cartesian or polar coordinates, you can clearly see the difference.

Brennen Fisher · Accepted Answer

Step 1            (      6      ,                        17          π                          12                    )        ,          (      5      ,                        5          π                          8                    )      Convert to Cartesian coordinates, remember the following formulas:                    x        =        r                  cos          θ                                        y        =        r                  sin          θ                    First coordinate:             (      6      ,                        17          π                          12                    )            x    =    6          cos              (                              17            π                    12                )                  y    =    6          sin              (                              17            π                    12                )                                          (          6                      cos                          (                                                17                  π                                12                            )                                ,          6                      sin                          (                                                17                  π                                12                            )                                )                    Second coordinate:             (      5      ,                        5          π                          8                    )            x    =    5          cos              (                              5            π                    8                )                  y    =    5          sin              (                              5            π                    8                )                                          (          5                      cos                          (                                                5                  π                                8                            )                                ,          5                      sin                          (                                                5                  π                                8                            )                                )                    Use the distance formula (Pythagorean Theorem) between these points:Distance            Distance        =                                        (            6                          cos                              (                                                      17                    π                                    12                                )                                      -            5                          cos                              (                                                      5                    π                                    8                                )                                      )                    2                +                              (            6                          sin                              (                                                      17                    π                                    12                                )                                      -            5                          sin                              (                                                      5                    π                                    8                                )                                      )                    2                    Distance             Distance               ≈    10.42119

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

Answered question

Answer & Explanation

New Questions in Integral Calculus