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Popular Trigonometria >

cos(2x-pi/6)=((sqrt(3)))/2 ,0<x<2pi

Solução

cos (2 x - \frac{π}{6}) = \frac{( 3 )}{2}, 0 < x < 2 π

Solução

x = \frac{π}{6}, x = π, x = \frac{7 π}{6}

Graus

x = 3 0^{\circ}, x = 18 0^{\circ}, x = 21 0^{\circ}

Passos da solução

cos (2 x - \frac{π}{6}) = \frac{( 3 )}{2}, 0 < x < 2 π

Soluções gerais para

cos (2 x - \frac{π}{6}) = \frac{3}{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}

2 x - \frac{π}{6} = \frac{π}{6} + 2 πn, 2 x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

2 x - \frac{π}{6} = \frac{π}{6} + 2 πn, 2 x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

Resolver

2 x - \frac{π}{6} = \frac{π}{6} + 2 πn : x = \frac{π}{6} + πn

2 x - \frac{π}{6} = \frac{π}{6} + 2 πn

Mova

\frac{π}{6}

para o lado direito

2 x - \frac{π}{6} = \frac{π}{6} + 2 πn

Adicionar

\frac{π}{6}

a ambos os lados

2 x - \frac{π}{6} + \frac{π}{6} = \frac{π}{6} + 2 πn + \frac{π}{6}

Simplificar

2 x - \frac{π}{6} + \frac{π}{6} = \frac{π}{6} + 2 πn + \frac{π}{6}

Simplificar

2 x - \frac{π}{6} + \frac{π}{6} : 2 x

2 x - \frac{π}{6} + \frac{π}{6}

Somar elementos similares:

- \frac{π}{6} + \frac{π}{6} = 0

= 2 x

Simplificar

\frac{π}{6} + 2 πn + \frac{π}{6} : \frac{π}{3} + 2 πn

\frac{π}{6} + 2 πn + \frac{π}{6}

Agrupar termos semelhantes

= \frac{π}{6} + \frac{π}{6} + 2 πn

Combinar as frações usando o mínimo múltiplo comum:

\frac{π}{3}

Aplicar a regra

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

= \frac{π + π}{6}

Somar elementos similares:

π + π = 2 π

= \frac{2 π}{6}

Eliminar o fator comum:

2

= \frac{π}{3}

= \frac{π}{3} + 2 πn

2 x = \frac{π}{3} + 2 πn

2 x = \frac{π}{3} + 2 πn

2 x = \frac{π}{3} + 2 πn

Dividir ambos os lados por

2

2 x = \frac{π}{3} + 2 πn

Dividir ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} : \frac{π}{6} + πn

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

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Aplicar as propriedades das frações:

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

= \frac{π}{3 \cdot 2}

Multiplicar os números:

3 \cdot 2 = 6

= \frac{π}{6}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

Resolver

2 x - \frac{π}{6} = \frac{11 π}{6} + 2 πn : x = πn + π

2 x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

Mova

\frac{π}{6}

para o lado direito

2 x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

Adicionar

\frac{π}{6}

a ambos os lados

2 x - \frac{π}{6} + \frac{π}{6} = \frac{11 π}{6} + 2 πn + \frac{π}{6}

Simplificar

2 x - \frac{π}{6} + \frac{π}{6} = \frac{11 π}{6} + 2 πn + \frac{π}{6}

Simplificar

2 x - \frac{π}{6} + \frac{π}{6} : 2 x

2 x - \frac{π}{6} + \frac{π}{6}

Somar elementos similares:

- \frac{π}{6} + \frac{π}{6} = 0

= 2 x

Simplificar

\frac{11 π}{6} + 2 πn + \frac{π}{6} : 2 πn + 2 π

\frac{11 π}{6} + 2 πn + \frac{π}{6}

Agrupar termos semelhantes

= 2 πn + \frac{π}{6} + \frac{11 π}{6}

Combinar as frações usando o mínimo múltiplo comum:

2 π

Aplicar a regra

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

= \frac{π + 11 π}{6}

Somar elementos similares:

π + 11 π = 12 π

= \frac{12 π}{6}

Dividir:

\frac{12}{6} = 2

= 2 π

= 2 πn + 2 π

2 x = 2 πn + 2 π

2 x = 2 πn + 2 π

2 x = 2 πn + 2 π

Dividir ambos os lados por

2

2 x = 2 πn + 2 π

Dividir ambos os lados por

2

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

Simplificar

x = πn + π

x = πn + π

x = \frac{π}{6} + πn, x = πn + π

Soluções para o intervalo

0 < x < 2 π

x = \frac{π}{6}, x = π, x = \frac{7 π}{6}

Gráfico

Exemplos populares

-1=tan(x)

sin(2x)=(sqrt(3))/2 ,0<= x<= 2pi

2tan(x)=1-tan^2(x)

3sin(θ)+3=2cos^2(θ)

cos(x)=-5/6