Pre-Calc/Math

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Use factoring, the quadratic formula, or identities to solve cos(x)+1=sin^(2)x. Find all solutions on the interval [0, 2pi)

  • Pre-Calc/Math -

    recall that
    sin^2 x + cos^2 x = 1
    therefore, we use this substitute the sin^2 x at the right side of equation:
    cos(x) + 1 = 1 - cos^2 x
    cos(x) = -cos^2 x
    cos(x) + cos^2 (x) = 0
    factoring,
    cos(x) [1 + cos(x)] = 0
    *for cos(x) = 0, the x values allowed are π/2 and 3π/2.
    *for (1 + cos(x)) = 0 or cos(x) = -1, the x value allowed is π.

    therefore,
    x = π/2, π, 3π/2

    hope this helps~ :)

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