For f ( t ) = ( cos t 2 , sin 2 t ) what is the distance between f ( π 4 ) and f ( π ) ?

Question

For             f              (        t        )              =          (                        cos          t                2            ,                        sin          2                t            )       what is the distance between             f              (                  π          4                )             and             f              (        π        )             ?

boomzwamhc · Accepted Answer

Step 1First, let us get the coordinates for each point.For point             f              (                  π          4                )            , we have            x      f        =                  cos                  (                      π            4                    )                    2                  y      f        =                  sin        2                    (                  π          4                )            As we know,             cos              (                  π          4                )              =          sin              (                  π          4                )              =          1                        2                                x      f        =          1              2                              2                                =                            2                    4                  y      f        =                  (                  1                                    2                                      )            2        =          1      2      For point             f              (        π        )             we have            x      f        =                  cos                  (          π          )                    2                  y      f        =                  sin        2                    (        π        )            We know that             cos              (        π        )              =    -    1   and that             sin              (        π        )              =    0   , so            x      f        =    -          1      2                  y      f        =    0  The distance between             (                                    2                          4            ;              1        2            )       and             (      -              1        2            ;      0      )       is given by            d      2        =                  (                                            2                                4                +                  1          2                )            2        +                  (                  1          2                )            2                  d      2        =          1      16                      (                              2                          +        2        )            2        +          1      4                  d      2        =          1      16              (      2      +      4                        2                    +      4      )        +          1      4                  d      2        =          1      16              (      6      +      4                        2                    )        +          1      4                  d      2        =                  3        +        2                              2                              8        +          1      4                  d      2        =                  3        +        2                              2                          +        2            8                  d      2        =                  5        +        2                              2                              8            d    =                                        5            +            2                                          2                                              8

For <mstyle displaystyle="true"> f ( t ) </mrow>

Answered question

Answer & Explanation

New Questions in Integral Calculus