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

Question

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

Hayley Mccarthy · Accepted Answer

Step 1Here,            f              (        t        )              =          (              sin        t            ,                                    cos            2                    t                t            )            ⇒          f              (                  π          4                )              =          (              sin                  (                      π            4                    )                    ,                                    cos            2                                (                          π              4                        )                                                π            4                              )        =          (              1                              2                              ,                                    1            2                                                π            4                              )        =          (              1                              2                              ,              2        π            )      Similarly,            f              (        π        )              =          (              sin        π            ,                                    cos            2                    π                π            )        =          (      0      ,                                    (            -            1            )                    2                π            )        =          (      0      ,              1        π            )      Distance Formula:If       A          (              x        1            ,              y        1            )                    and              B          (              x        2            .              y        2            )        ,   , then      d          (      A      ,      B      )        =                                        (                          x              1                        -                          x              2                        )                    2                +                              (                          x              2                        -                          y              2                        )                    2                          ⇒    d          (              f                  (                      π            4                    )                    ,              f                  (          π          )                    )        =                                        (                          1                                                2                                                      -            0            )                    2                +                              (                          2              π                        -                          1              π                        )                    2                      =                            1          2                +                  1                                    π              2

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