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Popular >

sin(x)cos(x)= 1/4

Solução

sin (x) cos (x) = \frac{1}{4}

Solução

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

Graus

x = 1 5^{\circ} + 18 0^{\circ} n, x = 7 5^{\circ} + 18 0^{\circ} n

Passos da solução

sin (x) cos (x) = \frac{1}{4}

Reeecreva usando identidades trigonométricas

sin (x) cos (x)

Utilizar a identidade trigonométrica do arco duplo:

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

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

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

\frac{sin ( 2 x )}{2} = \frac{1}{4}

Multiplicar ambos os lados por

2

\frac{sin ( 2 x )}{2} = \frac{1}{4}

Multiplicar ambos os lados por

2

\frac{2 sin ( 2 x )}{2} = \frac{1 \cdot 2}{4}

Simplificar

\frac{2 sin ( 2 x )}{2} = \frac{1 \cdot 2}{4}

Simplificar

\frac{2 sin ( 2 x )}{2} : sin (2 x)

\frac{2 sin ( 2 x )}{2}

Dividir:

\frac{2}{2} = 1

= sin (2 x)

Simplificar

\frac{1 \cdot 2}{4} : \frac{1}{2}

\frac{1 \cdot 2}{4}

Multiplicar os números:

1 \cdot 2 = 2

= \frac{2}{4}

Eliminar o fator comum:

2

= \frac{1}{2}

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

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

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

Soluções gerais para

sin (2 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}

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

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

Resolver

2 x = \frac{π}{6} + 2 πn : x = \frac{π}{12} + πn

2 x = \frac{π}{6} + 2 πn

Dividir ambos os lados por

2

2 x = \frac{π}{6} + 2 πn

Dividir ambos os lados por

2

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

Simplificar

\frac{2 x}{2} = \frac{\frac{π}{6}}{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}{6}}{2} + \frac{2 πn}{2} : \frac{π}{12} + πn

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

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

Aplicar as propriedades das frações:

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

= \frac{π}{6 \cdot 2}

Multiplicar os números:

6 \cdot 2 = 12

= \frac{π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{π}{12} + πn

x = \frac{π}{12} + πn

x = \frac{π}{12} + πn

x = \frac{π}{12} + πn

Resolver

2 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{12} + πn

2 x = \frac{5 π}{6} + 2 πn

Dividir ambos os lados por

2

2 x = \frac{5 π}{6} + 2 πn

Dividir ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2} : \frac{5 π}{12} + πn

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

\frac{\frac{5 π}{6}}{2} = \frac{5 π}{12}

\frac{\frac{5 π}{6}}{2}

Aplicar as propriedades das frações:

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

= \frac{5 π}{6 \cdot 2}

Multiplicar os números:

6 \cdot 2 = 12

= \frac{5 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{5 π}{12} + πn

x = \frac{5 π}{12} + πn

x = \frac{5 π}{12} + πn

x = \frac{5 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

Exemplos populares

12sin^2(x)-13sin(x)+3=0

12 sin^{2} (x) - 13 sin (x) + 3 = 0

sin(θ)= 1/(sqrt(2))

sin (θ) = \frac{1}{2}

csc^2(x)-1=0

csc^{2} (x) - 1 = 0

csc(θ)=(2sqrt(3))/3

csc (θ) = \frac{2 3}{3}

-sin(2x)=0

- sin (2 x) = 0