問31
(1)
sin θ - cos^{2}θ+ sin^{2}θ >= 0
2sin^{2}θ + sin θ - 1 >= 0
(2sin θ - 1)(sin θ + 1) >= 0
sin θ <= -1, 1/2 <= sin θ
0 <= θ < 2π
より
θ = 3π/2, π/6 <= θ <= 5π/6
(2)
sin θ - cos^{2}θ + sin^{2}θ = 0
2sin^{2}θ + sin θ - 1 = 0
(2sin θ - 1)(sin θ + 1) = 0
sin θ = 1/2, -1
0 <= θ < 2π
より
θ = π/6, 5π/6, 3π/2
(3)
cos^{2}θ - sin^{2}θ - 3cos θ -1 = 0
2cos^{2}θ -3cos θ -2 = 0
(cos θ - 2)(2cos θ + 1) = 0
cos θ = -1/2
0 <= θ < 2π
より
θ = 2π/3, 4π/3
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