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find the exact zeros of the function in the interval [0, 2π)
2 cot squared x + 3 csc x=0

  • trig -

    We know that
    1 + cot^2 Ø = csc^2 Ø
    so our equation is

    2(csc^ x - 1) + 3csc x = 0
    2 csc^2 x + 3csc x - 2 = 0
    (2cscx -1)(cscx + 2) = 0
    cscx = 1/2 or cscx = -2
    sinx = 2 (not possible) or sinx = -1/2

    so x must be in III or IV
    x = 7π/6 or 11π/6

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