How to find the exact values of cos(11pi/12) using the half angle formula?

Question

Metafune7re · Accepted Answer

Call             cos              (                              11            π                    12                )              =          cos      t                  cos      2        t    =          cos              (                              22            π                    12                )              =          cos              (                              11            π                    6                )              =          cos              (                              π                    6                )              =                  3            2      Put the trig identity to use:             cos      2        t    =    2                  cos        2            t        -    1              cos      2        t    =                  3            2        =    2                  cos        2            t        -    1        2                  cos        2            t        =    1    +                  3            2        =                  2        +                  3                    2                          cos        2            t        =                  2        +                  3                    4                  cos      t        =          cos              (                              11            π                    12                )              =    ±                            2          +                      3                              2        .  Since the arc ((11pi)/12) is located in Quadrant II, only the negative answer is accepted.            cos              (                              11            π                    12                )              =    -                            2          +                      3                              2      Check by calculator.      A    r    c          (                        11          π                12            )        =    165   deg-&amp;gt;             cos              (                              11            π                    12                )              =          cos      165        =    -    0.97    .        -          (                                    2            +                          3                                      2            )        =    -    0.97  .

How to find the exact values of cos(11pi/12) using the half angle formula?

Answered question

Answer & Explanation