Math/trig

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Solve the equation in the given Domain:

1-cos theta/ sin theta = sqr3, 0degrees <or equal to theta < 369 degrees


cos4x + cos 2x =0, 0<or equal to x < pi

  • Math/trig -

    Recall that

    1-cos theta/ sin theta = tan(theta/2)

    so, we want tan(theta/2) = sqrt(3)
    theta/2 = 60
    theta = 120

    Note that theta/2 = 240 also works, but that requires theta=480, outside the domain given.
    ___________________________

    2cos^2(2x) - 1 + cos(2x) = 0
    (2cos2x - 1)(cos2x + 1) = 0

    cos2x = 1/2, so 2x = 60,300, so x=30,150
    cos2x = -1, so 2x = 180, so x=90

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