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Trigonometry

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Find all solutions of the equation in the interval [0,2pi] algebraically.

sin^2x + cosx + 1 = 0

  • Trigonometry -

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

    cos^2 x - cos x - 2 = 0

    (cos x - 2)(cos x + 1) = 0
    cos x = 2 impossible, out of range
    so
    cos x = -1
    pi

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