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Find all solutions in the interval [0,2π)

Calculus
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sin^2(theta) + cos(theta) = 1

Mar 20th, 2015

sin^2 θ + cosθ = 1

1 - cos^2 θ + cosθ = 1

cosθ - cos^2 θ = 0

cosθ(1 - cosθ) = 0

cosθ = 0   ,   1 - cosθ = 0

θ = π/2, 3π/2                   cosθ = 1

                                 θ = 0

Hence θ = 0 , π/2 , 3π/2

Mar 20th, 2015

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