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Popular Trigonometria >

2-2cos^2(x/2)=2sin^2(x)

Solução

2 - 2 cos^{2} (\frac{x}{2}) = 2 sin^{2} (x)

Solução

x = 4 πn, x = 2 π + 4 πn, x = \frac{4 π}{3} + 4 πn, x = \frac{8 π}{3} + 4 πn, x = \frac{2 π + 8 πn}{3}, x = 2 π + \frac{8 πn}{3}, x = 8 πn, x = 4 π + 8 πn

Graus

x = 0^{\circ} + 72 0^{\circ} n, x = 36 0^{\circ} + 72 0^{\circ} n, x = 24 0^{\circ} + 72 0^{\circ} n, x = 48 0^{\circ} + 72 0^{\circ} n, x = 12 0^{\circ} + 48 0^{\circ} n, x = 36 0^{\circ} + 48 0^{\circ} n, x = 0^{\circ} + 144 0^{\circ} n, x = 72 0^{\circ} + 144 0^{\circ} n

Passos da solução

2 - 2 cos^{2} (\frac{x}{2}) = 2 sin^{2} (x)

Subtrair

2 sin^{2} (x)

de ambos os lados

2 - 2 cos^{2} (\frac{x}{2}) - 2 sin^{2} (x) = 0

Sea:

u = \frac{x}{2}

2 - 2 cos^{2} (u) - 2 sin^{2} (2 u) = 0

Reeecreva usando identidades trigonométricas

2 - 2 cos^{2} (u) - 2 sin^{2} (2 u)

Utilizar a identidade trigonométrica pitagórica:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= 2 - 2 (1 - sin^{2} (u)) - 2 sin^{2} (2 u)

Simplificar

2 - 2 (1 - sin^{2} (u)) - 2 sin^{2} (2 u) : 2 sin^{2} (u) - 2 sin^{2} (2 u)

2 - 2 (1 - sin^{2} (u)) - 2 sin^{2} (2 u)

Expandir

- 2 (1 - sin^{2} (u)) : - 2 + 2 sin^{2} (u)

- 2 (1 - sin^{2} (u))

Colocar os parênteses utilizando:

a (b - c) = ab - a c

a = - 2, b = 1, c = sin^{2} (u)

= - 2 \cdot 1 - (- 2) sin^{2} (u)

Aplicar as regras dos sinais

- (- a) = a

= - 2 \cdot 1 + 2 sin^{2} (u)

Multiplicar os números:

2 \cdot 1 = 2

= - 2 + 2 sin^{2} (u)

= 2 - 2 + 2 sin^{2} (u) - 2 sin^{2} (2 u)

2 - 2 = 0

= 2 sin^{2} (u) - 2 sin^{2} (2 u)

= 2 sin^{2} (u) - 2 sin^{2} (2 u)

- 2 sin^{2} (2 u) + 2 sin^{2} (u) = 0

Fatorar

- 2 sin^{2} (2 u) + 2 sin^{2} (u) : 2 (sin (u) + sin (2 u)) (sin (u) - sin (2 u))

- 2 sin^{2} (2 u) + 2 sin^{2} (u)

Fatorar o termo comum

2

= 2 (- sin^{2} (2 u) + sin^{2} (u))

Fatorar

sin^{2} (u) - sin^{2} (2 u) : (sin (u) + sin (2 u)) (sin (u) - sin (2 u))

sin^{2} (u) - sin^{2} (2 u)

Aplicar a regra da diferença de quadrados:

x^{2} - y^{2} = (x + y) (x - y)

sin^{2} (u) - sin^{2} (2 u) = (sin (u) + sin (2 u)) (sin (u) - sin (2 u))

= (sin (u) + sin (2 u)) (sin (u) - sin (2 u))

= 2 (sin (u) + sin (2 u)) (sin (u) - sin (2 u))

2 (sin (u) + sin (2 u)) (sin (u) - sin (2 u)) = 0

Resolver cada parte separadamente

sin (u) + sin (2 u) = 0 or sin (u) - sin (2 u) = 0

sin (u) + sin (2 u) = 0 : u = 2 πn, u = π + 2 πn, u = \frac{2 π}{3} + 2 πn, u = \frac{4 π}{3} + 2 πn

sin (u) + sin (2 u) = 0

Reeecreva usando identidades trigonométricas

sin (2 u) + sin (u)

Utilizar a identidade trigonométrica do arco duplo:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (u) cos (u) + sin (u)

sin (u) + 2 cos (u) sin (u) = 0

Fatorar

sin (u) + 2 cos (u) sin (u) : sin (u) (2 cos (u) + 1)

sin (u) + 2 cos (u) sin (u)

Fatorar o termo comum

sin (u)

= sin (u) (1 + 2 cos (u))

sin (u) (2 cos (u) + 1) = 0

Resolver cada parte separadamente

sin (u) = 0 or 2 cos (u) + 1 = 0

sin (u) = 0 : u = 2 πn, u = π + 2 πn

sin (u) = 0

Soluções gerais para

sin (u) = 0

sin (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

u = 0 + 2 πn, u = π + 2 πn

u = 0 + 2 πn, u = π + 2 πn

Resolver

u = 0 + 2 πn : u = 2 πn

u = 0 + 2 πn

0 + 2 πn = 2 πn

u = 2 πn

u = 2 πn, u = π + 2 πn

2 cos (u) + 1 = 0 : u = \frac{2 π}{3} + 2 πn, u = \frac{4 π}{3} + 2 πn

2 cos (u) + 1 = 0

Mova

1

para o lado direito

2 cos (u) + 1 = 0

Subtrair

1

de ambos os lados

2 cos (u) + 1 - 1 = 0 - 1

Simplificar

2 cos (u) = - 1

2 cos (u) = - 1

Dividir ambos os lados por

2

2 cos (u) = - 1

Dividir ambos os lados por

2

\frac{2 cos ( u )}{2} = \frac{- 1}{2}

Simplificar

cos (u) = - \frac{1}{2}

cos (u) = - \frac{1}{2}

Soluções gerais para

cos (u) = - \frac{1}{2}

cos (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

u = \frac{2 π}{3} + 2 πn, u = \frac{4 π}{3} + 2 πn

u = \frac{2 π}{3} + 2 πn, u = \frac{4 π}{3} + 2 πn

Combinar toda as soluções

u = 2 πn, u = π + 2 πn, u = \frac{2 π}{3} + 2 πn, u = \frac{4 π}{3} + 2 πn

sin (u) - sin (2 u) = 0 : u = \frac{π}{3} + \frac{4 πn}{3}, u = π + \frac{4 πn}{3}, u = 4 πn, u = 2 π + 4 πn

sin (u) - sin (2 u) = 0

Reeecreva usando identidades trigonométricas

- sin (2 u) + sin (u)

Use a identidade da transformação de soma em produto:

sin (s) - sin (t) = 2 sin (\frac{s - t}{2}) cos (\frac{s + t}{2})

= 2 sin (\frac{u - 2 u}{2}) cos (\frac{u + 2 u}{2})

Simplificar

2 sin (\frac{u - 2 u}{2}) cos (\frac{u + 2 u}{2}) : - 2 cos (\frac{3 u}{2}) sin (\frac{u}{2})

2 sin (\frac{u - 2 u}{2}) cos (\frac{u + 2 u}{2})

\frac{u - 2 u}{2} = - \frac{u}{2}

\frac{u - 2 u}{2}

Somar elementos similares:

u - 2 u = - u

= \frac{- u}{2}

Aplicar as propriedades das frações:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{u}{2}

= 2 sin (- \frac{u}{2}) cos (\frac{u + 2 u}{2})

Use a identidade de ângulo negativo:

sin (- x) = - sin (x)

= 2 cos (\frac{u + 2 u}{2}) (- sin (\frac{u}{2}))

Remover os parênteses:

(- a) = - a

= - 2 cos (\frac{u + 2 u}{2}) sin (\frac{u}{2})

Somar elementos similares:

u + 2 u = 3 u

= - 2 cos (\frac{3 u}{2}) sin (\frac{u}{2})

= - 2 cos (\frac{3 u}{2}) sin (\frac{u}{2})

- 2 cos (\frac{3 u}{2}) sin (\frac{u}{2}) = 0

Resolver cada parte separadamente

cos (\frac{3 u}{2}) = 0 or sin (\frac{u}{2}) = 0

cos (\frac{3 u}{2}) = 0 : u = \frac{π}{3} + \frac{4 πn}{3}, u = π + \frac{4 πn}{3}

cos (\frac{3 u}{2}) = 0

Soluções gerais para

cos (\frac{3 u}{2}) = 0

cos (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{3 u}{2} = \frac{π}{2} + 2 πn, \frac{3 u}{2} = \frac{3 π}{2} + 2 πn

\frac{3 u}{2} = \frac{π}{2} + 2 πn, \frac{3 u}{2} = \frac{3 π}{2} + 2 πn

Resolver

\frac{3 u}{2} = \frac{π}{2} + 2 πn : u = \frac{π}{3} + \frac{4 πn}{3}

\frac{3 u}{2} = \frac{π}{2} + 2 πn

Multiplicar ambos os lados por

2

\frac{3 u}{2} = \frac{π}{2} + 2 πn

Multiplicar ambos os lados por

2

\frac{2 \cdot 3 u}{2} = 2 \cdot \frac{π}{2} + 2 \cdot 2 πn

Simplificar

\frac{2 \cdot 3 u}{2} = 2 \cdot \frac{π}{2} + 2 \cdot 2 πn

Simplificar

\frac{2 \cdot 3 u}{2} : 3 u

\frac{2 \cdot 3 u}{2}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{6 u}{2}

Dividir:

\frac{6}{2} = 3

= 3 u

Simplificar

2 \cdot \frac{π}{2} + 2 \cdot 2 πn : π + 4 πn

2 \cdot \frac{π}{2} + 2 \cdot 2 πn

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{2}

Eliminar o fator comum:

2

= π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 4 πn

= π + 4 πn

3 u = π + 4 πn

3 u = π + 4 πn

3 u = π + 4 πn

Dividir ambos os lados por

3

3 u = π + 4 πn

Dividir ambos os lados por

3

\frac{3 u}{3} = \frac{π}{3} + \frac{4 πn}{3}

Simplificar

u = \frac{π}{3} + \frac{4 πn}{3}

u = \frac{π}{3} + \frac{4 πn}{3}

Resolver

\frac{3 u}{2} = \frac{3 π}{2} + 2 πn : u = π + \frac{4 πn}{3}

\frac{3 u}{2} = \frac{3 π}{2} + 2 πn

Multiplicar ambos os lados por

2

\frac{3 u}{2} = \frac{3 π}{2} + 2 πn

Multiplicar ambos os lados por

2

\frac{2 \cdot 3 u}{2} = 2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

Simplificar

\frac{2 \cdot 3 u}{2} = 2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

Simplificar

\frac{2 \cdot 3 u}{2} : 3 u

\frac{2 \cdot 3 u}{2}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{6 u}{2}

Dividir:

\frac{6}{2} = 3

= 3 u

Simplificar

2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn : 3 π + 4 πn

2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

2 \cdot \frac{3 π}{2} = 3 π

2 \cdot \frac{3 π}{2}

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 π 2}{2}

Eliminar o fator comum:

2

= 3 π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 4 πn

= 3 π + 4 πn

3 u = 3 π + 4 πn

3 u = 3 π + 4 πn

3 u = 3 π + 4 πn

Dividir ambos os lados por

3

3 u = 3 π + 4 πn

Dividir ambos os lados por

3

\frac{3 u}{3} = \frac{3 π}{3} + \frac{4 πn}{3}

Simplificar

u = π + \frac{4 πn}{3}

u = π + \frac{4 πn}{3}

u = \frac{π}{3} + \frac{4 πn}{3}, u = π + \frac{4 πn}{3}

sin (\frac{u}{2}) = 0 : u = 4 πn, u = 2 π + 4 πn

sin (\frac{u}{2}) = 0

Soluções gerais para

sin (\frac{u}{2}) = 0

sin (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{u}{2} = 0 + 2 πn, \frac{u}{2} = π + 2 πn

\frac{u}{2} = 0 + 2 πn, \frac{u}{2} = π + 2 πn

Resolver

\frac{u}{2} = 0 + 2 πn : u = 4 πn

\frac{u}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{u}{2} = 2 πn

Multiplicar ambos os lados por

2

\frac{u}{2} = 2 πn

Multiplicar ambos os lados por

2

\frac{2 u}{2} = 2 \cdot 2 πn

Simplificar

u = 4 πn

u = 4 πn

Resolver

\frac{u}{2} = π + 2 πn : u = 2 π + 4 πn

\frac{u}{2} = π + 2 πn

Multiplicar ambos os lados por

2

\frac{u}{2} = π + 2 πn

Multiplicar ambos os lados por

2

\frac{2 u}{2} = 2 π + 2 \cdot 2 πn

Simplificar

u = 2 π + 4 πn

u = 2 π + 4 πn

u = 4 πn, u = 2 π + 4 πn

Combinar toda as soluções

u = \frac{π}{3} + \frac{4 πn}{3}, u = π + \frac{4 πn}{3}, u = 4 πn, u = 2 π + 4 πn

Combinar toda as soluções

u = 2 πn, u = π + 2 πn, u = \frac{2 π}{3} + 2 πn, u = \frac{4 π}{3} + 2 πn, u = \frac{π}{3} + \frac{4 πn}{3}, u = π + \frac{4 πn}{3}, u = 4 πn, u = 2 π + 4 πn

Substituir na equação

u = \frac{x}{2}

\frac{x}{2} = 2 πn : x = 4 πn

\frac{x}{2} = 2 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = 2 πn

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 \cdot 2 πn

Simplificar

x = 4 πn

x = 4 πn

\frac{x}{2} = π + 2 πn : x = 2 π + 4 πn

\frac{x}{2} = π + 2 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = π + 2 πn

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 π + 2 \cdot 2 πn

Simplificar

x = 2 π + 4 πn

x = 2 π + 4 πn

\frac{x}{2} = \frac{2 π}{3} + 2 πn : x = \frac{4 π}{3} + 4 πn

\frac{x}{2} = \frac{2 π}{3} + 2 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = \frac{2 π}{3} + 2 πn

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn

Simplificar

\frac{2 x}{2} = 2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn : \frac{4 π}{3} + 4 πn

2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn

2 \cdot \frac{2 π}{3} = \frac{4 π}{3}

2 \cdot \frac{2 π}{3}

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 π 2}{3}

Multiplicar os números:

2 \cdot 2 = 4

= \frac{4 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 4 πn

= \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

\frac{x}{2} = \frac{4 π}{3} + 2 πn : x = \frac{8 π}{3} + 4 πn

\frac{x}{2} = \frac{4 π}{3} + 2 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = \frac{4 π}{3} + 2 πn

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 \cdot \frac{4 π}{3} + 2 \cdot 2 πn

Simplificar

\frac{2 x}{2} = 2 \cdot \frac{4 π}{3} + 2 \cdot 2 πn

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 \cdot \frac{4 π}{3} + 2 \cdot 2 πn : \frac{8 π}{3} + 4 πn

2 \cdot \frac{4 π}{3} + 2 \cdot 2 πn

2 \cdot \frac{4 π}{3} = \frac{8 π}{3}

2 \cdot \frac{4 π}{3}

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 π 2}{3}

Multiplicar os números:

4 \cdot 2 = 8

= \frac{8 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 4 πn

= \frac{8 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn

\frac{x}{2} = \frac{π}{3} + \frac{4 πn}{3} : x = \frac{2 π + 8 πn}{3}

\frac{x}{2} = \frac{π}{3} + \frac{4 πn}{3}

Multiplicar ambos os lados por

2

\frac{x}{2} = \frac{π}{3} + \frac{4 πn}{3}

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 \cdot \frac{π}{3} + 2 \cdot \frac{4 πn}{3}

Simplificar

\frac{2 x}{2} = 2 \cdot \frac{π}{3} + 2 \cdot \frac{4 πn}{3}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 \cdot \frac{π}{3} + 2 \cdot \frac{4 πn}{3} : \frac{2 π + 8 πn}{3}

2 \cdot \frac{π}{3} + 2 \cdot \frac{4 πn}{3}

2 \cdot \frac{π}{3} = \frac{2 π}{3}

2 \cdot \frac{π}{3}

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{3}

2 \cdot \frac{4 πn}{3} = \frac{8 πn}{3}

2 \cdot \frac{4 πn}{3}

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 πn \cdot 2}{3}

Multiplicar os números:

4 \cdot 2 = 8

= \frac{8 πn}{3}

= \frac{2 π}{3} + \frac{8 πn}{3}

Aplicar a regra

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 π + 8 πn}{3}

x = \frac{2 π + 8 πn}{3}

x = \frac{2 π + 8 πn}{3}

x = \frac{2 π + 8 πn}{3}

\frac{x}{2} = π + \frac{4 πn}{3} : x = 2 π + \frac{8 πn}{3}

\frac{x}{2} = π + \frac{4 πn}{3}

Multiplicar ambos os lados por

2

\frac{x}{2} = π + \frac{4 πn}{3}

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 π + 2 \cdot \frac{4 πn}{3}

Simplificar

\frac{2 x}{2} = 2 π + 2 \cdot \frac{4 πn}{3}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 π + 2 \cdot \frac{4 πn}{3} : 2 π + \frac{8 πn}{3}

2 π + 2 \cdot \frac{4 πn}{3}

2 \cdot \frac{4 πn}{3} = \frac{8 πn}{3}

2 \cdot \frac{4 πn}{3}

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 πn \cdot 2}{3}

Multiplicar os números:

4 \cdot 2 = 8

= \frac{8 πn}{3}

= 2 π + \frac{8 πn}{3}

x = 2 π + \frac{8 πn}{3}

x = 2 π + \frac{8 πn}{3}

x = 2 π + \frac{8 πn}{3}

\frac{x}{2} = 4 πn : x = 8 πn

\frac{x}{2} = 4 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = 4 πn

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 \cdot 4 πn

Simplificar

x = 8 πn

x = 8 πn

\frac{x}{2} = 2 π + 4 πn : x = 4 π + 8 πn

\frac{x}{2} = 2 π + 4 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = 2 π + 4 πn

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 \cdot 2 π + 2 \cdot 4 πn

Simplificar

x = 4 π + 8 πn

x = 4 π + 8 πn

x = 4 πn, x = 2 π + 4 πn, x = \frac{4 π}{3} + 4 πn, x = \frac{8 π}{3} + 4 πn, x = \frac{2 π + 8 πn}{3}, x = 2 π + \frac{8 πn}{3}, x = 8 πn, x = 4 π + 8 πn

Junte intervalos que se sobrepoem

x = 4 πn, x = 2 π + 4 πn, x = \frac{4 π}{3} + 4 πn, x = \frac{8 π}{3} + 4 πn, x = \frac{2 π + 8 πn}{3}, x = 2 π + \frac{8 πn}{3}, x = 8 πn, x = 4 π + 8 πn

Gráfico

Exemplos populares

3tanh^2(x)=5sech(x)+1

3 tanh^{2} (x) = 5 sech (x) + 1

tan(θ)= 5/7

tan (θ) = \frac{5}{7}

(cot(x)-1)(sqrt(3)tan(x)+1)=0

(cot (x) - 1) (3 tan (x) + 1) = 0

cos(2θ-pi/2)=(sqrt(2))/2

cos (2 θ - \frac{π}{2}) = \frac{2}{2}

tan^3(x)+tan^2(x)-3tan(x)=3

tan^{3} (x) + tan^{2} (x) - 3 tan (x) = 3