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EloraAndreote
@EloraAndreote
May 2020
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Resolver a equação Cos x = Cos (2x) com X E [0,2
π]
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Cos x = cos(2x)
cos x = 2 cos²x -1
2 cos²x - cos x -1 = 0
resolvendo a equação
Δ=(-1)² -4.2.(-1) = 9
cos x= (1 - 3)/4 = -2/4 = -1/2
ou
cos x= (1 + 3)/4 = 1
Se cox x = 1 ==> x = 0
Se cos x = -1/2 ==> x = 2π/3 ou x = 4π/3
S = { 0, 2π/3 , 4π/3 }
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Lista de comentários
cos x = 2 cos²x -1
2 cos²x - cos x -1 = 0
resolvendo a equação
Δ=(-1)² -4.2.(-1) = 9
cos x= (1 - 3)/4 = -2/4 = -1/2
ou
cos x= (1 + 3)/4 = 1
Se cox x = 1 ==> x = 0
Se cos x = -1/2 ==> x = 2π/3 ou x = 4π/3
S = { 0, 2π/3 , 4π/3 }