# 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 76 months agoFavourite answer
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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