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Find the solutions for sec^2x+secx=2 that fit into the interval [0, 2pi]

I figured out that pi/3 (after factoring and switching things around) was a solution, but then I got stuck on cos x = 1/3.

  • Pre-Calculus -


    why don't you factor it with the secant as is
    sec^2 x + secx - 2 = 0
    (secx + 2)(secx-1) = 0
    secx = -2 or secx = 1
    cosx = -1/2 or cosx = 1

    from cosx = -1/2, x = 120º (2pi/3) or 240º (4pi/3)
    from cosx = 1, x = 0 or 360º (0 or 2pi)

  • Pre-Calculus -

    The answers in the back of my book are pi/3,pi, and 5pi/3

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