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Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places. (Enter your answers as a comma-separated list.)

10 sin^2 x = 3 sin x + 4; [0, 2π)

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  1. 10 sin^2 x - 3sinx - 4 = 0
    (2sinx + 1)(5sinx - 4) = 0
    sinx = -1/2 or sinx = 4/5

    if sinx = -1/2, (x must be in III or IV)
    x = 210° or 330°

    if sinx = 4/5 , (x must be in I or II)
    x = 53.1301 or x = 126.8699°

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