F asked in Science & MathematicsMathematics · 6 months ago

Find the exact value of all angles θ in the interval [0,2π) that satisfy the equations. 2cos(2θ)+1=0?

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    Lv 7
    6 months ago
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    2 cos 2θ + 1 = 0

    cos 2θ = -¹⁄₂

    // Substitute for cos 2θ using

    // the double-angle formula:

    // cos 2θ = 2 cos² θ - 1

    2 cos² θ - 1 = -¹⁄₂

    cos² θ = ¹⁄₄

    cos θ = ± ¹⁄₂

    θ = cos⁻¹ ± ¹⁄₂

    θ = 120°, 60°

    // 120° = 2π/3 and 60° = π/3

    So,

    θ = π/3, 2π/3..................ANS

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