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Math Help - Find Exact solution over the interval [0.2pi)

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    Find Exact solution over the interval [0.2pi)

    I need to get the exact solutions over the interval [0,2pi)

    Sin 3x= -1


    I have the intervals 0< x < 2pi

    I am having trouble getting the first set of numbers with this inequality.
    I have that the angle is 30 degrees of pi/6.

    And the answer book says i should get

    pi/6, 7pi/6, 13pi/6, 19pi/6, 25pi/6, and 31pi/6

    I can get 4 of these by adding 2pi to each one, but i can't get 7pi/6 or 25pi/6.

    Can anyone help? Thanks!
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    Quote Originally Posted by KoolFlair View Post
    I need to get the exact solutions over the interval [0,2pi)

    Sin 3x= -1


    I have the intervals 0< x < 2pi

    I am having trouble getting the first set of numbers with this inequality.
    I have that the angle is 30 degrees of pi/6.

    And the answer book says i should get

    pi/6, 7pi/6, 13pi/6, 19pi/6, 25pi/6, and 31pi/6

    I can get 4 of these by adding 2pi to each one, but i can't get 7pi/6 or 25pi/6.

    Can anyone help? Thanks!
    I disagree with the book's solution.

    0 \le x < 2\pi

    0 \le 3x < 6\pi

    \sin(3x) = -1

    3x = \frac{3\pi}{2} \, , \,   \frac{7\pi}{2} \, , \,    \frac{11\pi}{2}

    x = \frac{\pi}{2} \, , \, \frac{7\pi}{6} \, , \,  \frac{11\pi}{6}
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