How to find the exact values of sin ( u 2 ) , cos ( u 2 ) , tan ( u 2 ) using the half angle formulas given sin u = 5 13 , π 2 &lt; u &lt; π ?

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How to find the exact values of             sin              (                  u          2                )              ,          cos              (                  u          2                )              ,          tan              (                  u          2                )             using the half angle formulas given             sin      u        =          5      13        ,          π      2        &amp;lt;    u    &amp;lt;    π  ?

planeiaxuf · Accepted Answer

sin      u        =          5      13      . First, find cos u.                    cos        2            u        =    1    -                  sin        2            u        =    1    -          25      169        =          144      169       --&amp;gt;             cos      u        =    ±          12      13      .Since u is in Quadrant 2, then, cos u &amp;lt; 0.            cos      u        =    -          12      13      .To find             cos              (                  u          2                )            , trigonometric identity in use      2                  cos        2                    (                  u          2                )              =    1    +          cos      u        =    1    -          12      13        =          1      13                          cos        2                    (                  u          2                )              =          1      26       --&amp;gt;             cos              (                  u          2                )              =    ±          1              26            .Sin u is in Quadrant 2, then             u      2       is in Quadrant 1, and             cos              (                  u          2                )             is positive:            cos              (                  u          2                )              =          1                        26                      =                  26            26      To find             sin              (                  u          2                )            , apply the trig identity:            sin      u        =    2          sin              (                  u          2                )              .          cos              (                  u          2                )                        sin              (                  u          2                )              =                            sin          u                            2                  cos                      (                          u              2                        )                                =          (              5        13            )              (                        26                2            )        =                  5                  26                    26                  tan              (                  u          2                )              =                            sin                      (                          u              2                        )                                                cos                      (                          u              2                        )                                =          (                        5                      26                          26            )              (              26            )        =    5

How to find the exact values of sin ( u 2 ) , cos (...

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