Re-express the following as a rational number, that is a number of the form n/m, where m and n are integers: 9 sinh ⁡ ( ln ⁡ 12 )

Question

Re-express the following as a rational number, that is a number of the form n/m, where m and n are integers:  9  sinh  ⁡  (  ln  ⁡  12  )

lesinetzgl5 · Accepted Answer

Given equation is   9  sinh  ⁡  (  ln  ⁡  12  )Formula:  sinh  ⁡  x  =            (              e        x            )      −      (              e                  −          x                    )        2      If   x  =  ln  ⁡  y  ,    sinh  ⁡  (  ln  ⁡  y  )  =            (              e                  ln          ⁡          y                    )      −      (              e                  −          ln          ⁡          y                    )        2      =            (      y      −      (              1        y            )        2    (   since       e          ln      ⁡      x      =      x          =                              y          2                −        1            y        2      =            (              y        2            −      1      )              2      y      So  =  9  sinh  ⁡  (  ln  ⁡  12  )    =  9                    12        2            −      1              2      ×      12          =            9      ×      (      144      −      1      )        24      =            9      ×      143        24      =            3      ×      143        8      =      429    8

Re-express the following as a rational number, that is a number of the form n/m, where m and n are integers: 9sinh (ln12)

Answered question

Answer & Explanation

New Questions in Trigonometry