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sin(4x)=-(sqrt(2))/2

Solución

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

Solución

x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

+1

Grados

x = 56.2 5^{\circ} + 9 0^{\circ} n, x = 78.7 5^{\circ} + 9 0^{\circ} n

Pasos de solución

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

Soluciones generales para

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

tabla de valores periódicos con

2 πn

intervalos:

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}

4 x = \frac{5 π}{4} + 2 πn, 4 x = \frac{7 π}{4} + 2 πn

4 x = \frac{5 π}{4} + 2 πn, 4 x = \frac{7 π}{4} + 2 πn

Resolver

4 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{16} + \frac{πn}{2}

4 x = \frac{5 π}{4} + 2 πn

Dividir ambos lados entre

4

4 x = \frac{5 π}{4} + 2 πn

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{\frac{5 π}{4}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} = \frac{\frac{5 π}{4}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{\frac{5 π}{4}}{4} + \frac{2 πn}{4} : \frac{5 π}{16} + \frac{πn}{2}

\frac{\frac{5 π}{4}}{4} + \frac{2 πn}{4}

\frac{\frac{5 π}{4}}{4} = \frac{5 π}{16}

\frac{\frac{5 π}{4}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{5 π}{4 \cdot 4}

Multiplicar los numeros:

4 \cdot 4 = 16

= \frac{5 π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{5 π}{16} + \frac{πn}{2}

x = \frac{5 π}{16} + \frac{πn}{2}

x = \frac{5 π}{16} + \frac{πn}{2}

x = \frac{5 π}{16} + \frac{πn}{2}

Resolver

4 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{16} + \frac{πn}{2}

4 x = \frac{7 π}{4} + 2 πn

Dividir ambos lados entre

4

4 x = \frac{7 π}{4} + 2 πn

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{\frac{7 π}{4}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} = \frac{\frac{7 π}{4}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{\frac{7 π}{4}}{4} + \frac{2 πn}{4} : \frac{7 π}{16} + \frac{πn}{2}

\frac{\frac{7 π}{4}}{4} + \frac{2 πn}{4}

\frac{\frac{7 π}{4}}{4} = \frac{7 π}{16}

\frac{\frac{7 π}{4}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{7 π}{4 \cdot 4}

Multiplicar los numeros:

4 \cdot 4 = 16

= \frac{7 π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{7 π}{16} + \frac{πn}{2}

x = \frac{7 π}{16} + \frac{πn}{2}

x = \frac{7 π}{16} + \frac{πn}{2}

x = \frac{7 π}{16} + \frac{πn}{2}

x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

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