I need to solve the following equation. The answer should be 7pi/12, 19pi/12, 3pi/4, and 7pi/4
cos(2x - pi/3) = -sqrt3/2
cos(2x - pi/3) = -sqrt3/2
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cos(2x - pi/3) = -sqrt3/2
2x-π/3 = arccos(-√3/2) = 5π/6 + 2nπ, 7π/6 + 2nπ
2x = 5π/6 + 2π/6 + 2nπ, 7π/6 + 2π/6 + 2nπ
2x = 7π/6 + 2nπ, 9π/6 + 2nπ = 7π/6 + 2nπ, 3π/2 + 2nπ
x = 7π/12 + nπ, 3π/4 + nπ
n = 0 : x = 7π/12, 3π/4
n = 1 : x = 19π/12, 7π/4
n = 2 : discard since x > 2π
x = 7π/12, 3π/4, 19π/12, 7π/4
x = 105°, 135°, 285°, 315°
2x-π/3 = arccos(-√3/2) = 5π/6 + 2nπ, 7π/6 + 2nπ
2x = 5π/6 + 2π/6 + 2nπ, 7π/6 + 2π/6 + 2nπ
2x = 7π/6 + 2nπ, 9π/6 + 2nπ = 7π/6 + 2nπ, 3π/2 + 2nπ
x = 7π/12 + nπ, 3π/4 + nπ
n = 0 : x = 7π/12, 3π/4
n = 1 : x = 19π/12, 7π/4
n = 2 : discard since x > 2π
x = 7π/12, 3π/4, 19π/12, 7π/4
x = 105°, 135°, 285°, 315°