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pre calc

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solve the equation
1+4sin(x)=4cos^2(x)

  • pre calc -

    without a graphing utility

  • pre calc -

    1+4sin(x)=4cos^2(x)
    1+4sinx = 4(1 - sin^2 x)
    4sin^2 x + 4sinx -3 = 0
    (2sinx - 1)(2sinx + 3) = 0
    sinx = 1/2 or sinx = -3/2
    the last part is not possible since sinx is between -1 and +1

    so sinx = 1/2
    x must be in quadrants I or II
    I know sin 30° = 1/2
    so x = 30° or 150°
    in radians
    x = π/6 or x = 5π/6

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