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Popular >

6cos(6x)=3

Solução

6 cos (6 x) = 3

Solução

x = \frac{π}{18} + \frac{πn}{3}, x = \frac{5 π}{18} + \frac{πn}{3}

+1

Graus

x = 1 0^{\circ} + 6 0^{\circ} n, x = 5 0^{\circ} + 6 0^{\circ} n

Passos da solução

6 cos (6 x) = 3

Dividir ambos os lados por

6

6 cos (6 x) = 3

Dividir ambos os lados por

6

\frac{6 cos ( 6 x )}{6} = \frac{3}{6}

Simplificar

cos (6 x) = \frac{1}{2}

cos (6 x) = \frac{1}{2}

Soluções gerais para

cos (6 x) = \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}

6 x = \frac{π}{3} + 2 πn, 6 x = \frac{5 π}{3} + 2 πn

6 x = \frac{π}{3} + 2 πn, 6 x = \frac{5 π}{3} + 2 πn

Resolver

6 x = \frac{π}{3} + 2 πn : x = \frac{π}{18} + \frac{πn}{3}

6 x = \frac{π}{3} + 2 πn

Dividir ambos os lados por

6

6 x = \frac{π}{3} + 2 πn

Dividir ambos os lados por

6

\frac{6 x}{6} = \frac{\frac{π}{3}}{6} + \frac{2 πn}{6}

Simplificar

\frac{6 x}{6} = \frac{\frac{π}{3}}{6} + \frac{2 πn}{6}

Simplificar

\frac{6 x}{6} : x

\frac{6 x}{6}

Dividir:

\frac{6}{6} = 1

= x

Simplificar

\frac{\frac{π}{3}}{6} + \frac{2 πn}{6} : \frac{π}{18} + \frac{πn}{3}

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

\frac{\frac{π}{3}}{6} = \frac{π}{18}

\frac{\frac{π}{3}}{6}

Aplicar as propriedades das frações:

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

= \frac{π}{3 \cdot 6}

Multiplicar os números:

3 \cdot 6 = 18

= \frac{π}{18}

\frac{2 πn}{6} = \frac{πn}{3}

\frac{2 πn}{6}

Eliminar o fator comum:

2

= \frac{πn}{3}

= \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

Resolver

6 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{18} + \frac{πn}{3}

6 x = \frac{5 π}{3} + 2 πn

Dividir ambos os lados por

6

6 x = \frac{5 π}{3} + 2 πn

Dividir ambos os lados por

6

\frac{6 x}{6} = \frac{\frac{5 π}{3}}{6} + \frac{2 πn}{6}

Simplificar

\frac{6 x}{6} = \frac{\frac{5 π}{3}}{6} + \frac{2 πn}{6}

Simplificar

\frac{6 x}{6} : x

\frac{6 x}{6}

Dividir:

\frac{6}{6} = 1

= x

Simplificar

\frac{\frac{5 π}{3}}{6} + \frac{2 πn}{6} : \frac{5 π}{18} + \frac{πn}{3}

\frac{\frac{5 π}{3}}{6} + \frac{2 πn}{6}

\frac{\frac{5 π}{3}}{6} = \frac{5 π}{18}

\frac{\frac{5 π}{3}}{6}

Aplicar as propriedades das frações:

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

= \frac{5 π}{3 \cdot 6}

Multiplicar os números:

3 \cdot 6 = 18

= \frac{5 π}{18}

\frac{2 πn}{6} = \frac{πn}{3}

\frac{2 πn}{6}

Eliminar o fator comum:

2

= \frac{πn}{3}

= \frac{5 π}{18} + \frac{πn}{3}

x = \frac{5 π}{18} + \frac{πn}{3}

x = \frac{5 π}{18} + \frac{πn}{3}

x = \frac{5 π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}, x = \frac{5 π}{18} + \frac{πn}{3}

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