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sin(8x)= 1/2

Solução

sin (8 x) = \frac{1}{2}

Solução

x = \frac{π}{48} + \frac{πn}{4}, x = \frac{5 π}{48} + \frac{πn}{4}

+1

Graus

x = 3.7 5^{\circ} + 4 5^{\circ} n, x = 18.7 5^{\circ} + 4 5^{\circ} n

Passos da solução

sin (8 x) = \frac{1}{2}

Soluções gerais para

sin (8 x) = \frac{1}{2}

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}

8 x = \frac{π}{6} + 2 πn, 8 x = \frac{5 π}{6} + 2 πn

8 x = \frac{π}{6} + 2 πn, 8 x = \frac{5 π}{6} + 2 πn

Resolver

8 x = \frac{π}{6} + 2 πn : x = \frac{π}{48} + \frac{πn}{4}

8 x = \frac{π}{6} + 2 πn

Dividir ambos os lados por

8

8 x = \frac{π}{6} + 2 πn

Dividir ambos os lados por

8

\frac{8 x}{8} = \frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

Simplificar

\frac{8 x}{8} = \frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

Simplificar

\frac{8 x}{8} : x

\frac{8 x}{8}

Dividir:

\frac{8}{8} = 1

= x

Simplificar

\frac{\frac{π}{6}}{8} + \frac{2 πn}{8} : \frac{π}{48} + \frac{πn}{4}

\frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

\frac{\frac{π}{6}}{8} = \frac{π}{48}

\frac{\frac{π}{6}}{8}

Aplicar as propriedades das frações:

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

= \frac{π}{6 \cdot 8}

Multiplicar os números:

6 \cdot 8 = 48

= \frac{π}{48}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

Eliminar o fator comum:

2

= \frac{πn}{4}

= \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

Resolver

8 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{48} + \frac{πn}{4}

8 x = \frac{5 π}{6} + 2 πn

Dividir ambos os lados por

8

8 x = \frac{5 π}{6} + 2 πn

Dividir ambos os lados por

8

\frac{8 x}{8} = \frac{\frac{5 π}{6}}{8} + \frac{2 πn}{8}

Simplificar

\frac{8 x}{8} = \frac{\frac{5 π}{6}}{8} + \frac{2 πn}{8}

Simplificar

\frac{8 x}{8} : x

\frac{8 x}{8}

Dividir:

\frac{8}{8} = 1

= x

Simplificar

\frac{\frac{5 π}{6}}{8} + \frac{2 πn}{8} : \frac{5 π}{48} + \frac{πn}{4}

\frac{\frac{5 π}{6}}{8} + \frac{2 πn}{8}

\frac{\frac{5 π}{6}}{8} = \frac{5 π}{48}

\frac{\frac{5 π}{6}}{8}

Aplicar as propriedades das frações:

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

= \frac{5 π}{6 \cdot 8}

Multiplicar os números:

6 \cdot 8 = 48

= \frac{5 π}{48}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

Eliminar o fator comum:

2

= \frac{πn}{4}

= \frac{5 π}{48} + \frac{πn}{4}

x = \frac{5 π}{48} + \frac{πn}{4}

x = \frac{5 π}{48} + \frac{πn}{4}

x = \frac{5 π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}, x = \frac{5 π}{48} + \frac{πn}{4}

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