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Popular Trigonometría >

sec(4x)-2/(sqrt(3))=0

Solución

sec (4 x) - \frac{2}{3} = 0

Solución

x = \frac{π}{24} + \frac{πn}{2}, x = \frac{11 π}{24} + \frac{πn}{2}

Grados

x = 7. 5^{\circ} + 9 0^{\circ} n, x = 82. 5^{\circ} + 9 0^{\circ} n

Pasos de solución

sec (4 x) - \frac{2}{3} = 0

Desplace

\frac{2}{3}

a la derecha

sec (4 x) - \frac{2}{3} = 0

Sumar

\frac{2}{3}

a ambos lados

sec (4 x) - \frac{2}{3} + \frac{2}{3} = 0 + \frac{2}{3}

Simplificar

sec (4 x) - \frac{2}{3} + \frac{2}{3} = 0 + \frac{2}{3}

Simplificar

sec (4 x) - \frac{2}{3} + \frac{2}{3} : sec (4 x)

sec (4 x) - \frac{2}{3} + \frac{2}{3}

Sumar elementos similares:

- \frac{2}{3} + \frac{2}{3} = 0

= sec (4 x)

Simplificar

0 + \frac{2}{3} : \frac{2 3}{3}

0 + \frac{2}{3}

0 + \frac{2}{3} = \frac{2}{3}

= \frac{2}{3}

Racionalizar

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

Multiplicar por el conjugado

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Aplicar las leyes de los exponentes:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

= \frac{2 3}{3}

sec (4 x) = \frac{2 3}{3}

sec (4 x) = \frac{2 3}{3}

sec (4 x) = \frac{2 3}{3}

Soluciones generales para

sec (4 x) = \frac{2 3}{3}

sec (x)

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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

4 x = \frac{π}{6} + 2 πn, 4 x = \frac{11 π}{6} + 2 πn

4 x = \frac{π}{6} + 2 πn, 4 x = \frac{11 π}{6} + 2 πn

Resolver

4 x = \frac{π}{6} + 2 πn : x = \frac{π}{24} + \frac{πn}{2}

4 x = \frac{π}{6} + 2 πn

Dividir ambos lados entre

4

4 x = \frac{π}{6} + 2 πn

Dividir ambos lados entre

4

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

Simplificar

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

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{\frac{π}{6}}{4} + \frac{2 πn}{4} : \frac{π}{24} + \frac{πn}{2}

\frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

\frac{\frac{π}{6}}{4} = \frac{π}{24}

\frac{\frac{π}{6}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{6 \cdot 4}

Multiplicar los numeros:

6 \cdot 4 = 24

= \frac{π}{24}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}

Resolver

4 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{24} + \frac{πn}{2}

4 x = \frac{11 π}{6} + 2 πn

Dividir ambos lados entre

4

4 x = \frac{11 π}{6} + 2 πn

Dividir ambos lados entre

4

\frac{4 x}{4} = \frac{\frac{11 π}{6}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} = \frac{\frac{11 π}{6}}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{\frac{11 π}{6}}{4} + \frac{2 πn}{4} : \frac{11 π}{24} + \frac{πn}{2}

\frac{\frac{11 π}{6}}{4} + \frac{2 πn}{4}

\frac{\frac{11 π}{6}}{4} = \frac{11 π}{24}

\frac{\frac{11 π}{6}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{11 π}{6 \cdot 4}

Multiplicar los numeros:

6 \cdot 4 = 24

= \frac{11 π}{24}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{11 π}{24} + \frac{πn}{2}

x = \frac{11 π}{24} + \frac{πn}{2}

x = \frac{11 π}{24} + \frac{πn}{2}

x = \frac{11 π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}, x = \frac{11 π}{24} + \frac{πn}{2}

Gráfica

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