Confusion with trigonometric equation 6 sin 2 ⁡ x = 1 0 ≤ x ≤ 2 π sin 2 ⁡ x = 1 / 6 sin ⁡ x = 1 / 6 sin ⁡ a = 1 / 6 a = 0.420 so x is 0.420 and 2.721According to the key at the back of the book there are supposed to be 2 more answers; 3.56 and 5.86. Could someone explain where I went wrong?

Question

Confusion with trigonometric equation                    6                  sin          2                ⁡        x                            =        1                    0        ≤        x        ≤        2        π                                      sin          2                ⁡        x                            =        1                  /                6                            sin        ⁡        x                            =        1                  /                          6                                    sin        ⁡        a                            =        1                  /                          6                                    a                            =        0.420            so   x is   0.420 and   2.721According to the key at the back of the book there are supposed to be 2 more answers;   3.56 and   5.86. Could someone explain where I went wrong?

Kalmukujobvg · Accepted Answer

If the trigonometric equation is supposed to be   6      sin    2    ⁡  x  =  1      sin    2    ⁡  x  =      1    6    ,like you said. However, when taking square root of both sides, we must consider all square roots and not just the principal square root.  sin  ⁡      x    =  ±      1          6        sin  ⁡      x    =  ±            6        6    x  =      sin          −      1        ⁡      (    ±                  6            6        )

Jonas Huff · Accepted Answer

The Solutions are given by  x  =  π  −      sin          −      1        ⁡      (          1              6              )    ∨  x  =  2  π  −      sin          −      1        ⁡      (          1              6              )    ∨  x  =      sin          −      1        ⁡      (          1              6              )    ∨  x  =  π  +      sin          −      1        ⁡      (          1              6              )

Confusion with trigonometric equation 6 sin^2 x=1 0 <= x <= 2 pi sin^2 x=1/6 sin x= 1/sqrt6 sin a=1/sqrt6 a=0.420 so x is 0.420 and 2.721

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