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Popular >

cos(2x)<=-(sqrt(3))/2

Solución

cos (2 x) \leq - \frac{3}{2}

Solución

\frac{5 π}{12} + πn \leq x \leq \frac{7 π}{12} + πn

Notación de intervalos

[\frac{5 π}{12} + πn, \frac{7 π}{12} + πn]

Notación decimal

1.30899 \dots + πn \leq x \leq 1.83259 \dots + πn

Pasos de solución

cos (2 x) \leq - \frac{3}{2}

Para

cos (x) \leq a

, si

- 1 < a < 1

entonces

arccos (a) + 2 πn \leq x \leq 2 π - arccos (a) + 2 πn

arccos (- \frac{3}{2}) + 2 πn \leq 2 x \leq 2 π - arccos (- \frac{3}{2}) + 2 πn

a \leq u \leq b

entonces

a \leq u and u \leq b

arccos (- \frac{3}{2}) + 2 πn \leq 2 x and 2 x \leq 2 π - arccos (- \frac{3}{2}) + 2 πn

arccos (- \frac{3}{2}) + 2 πn \leq 2 x : x \geq \frac{5 π}{12} + πn

arccos (- \frac{3}{2}) + 2 πn \leq 2 x

Intercambiar lados

2 x \geq arccos (- \frac{3}{2}) + 2 πn

Simplificar

arccos (- \frac{3}{2}) + 2 πn : \frac{5 π}{6} + 2 πn

arccos (- \frac{3}{2}) + 2 πn

Utilizar la siguiente identidad trivial:

arccos (- \frac{3}{2}) = \frac{5 π}{6}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{5 π}{6} + 2 πn

2 x \geq \frac{5 π}{6} + 2 πn

Dividir ambos lados entre

2

2 x \geq \frac{5 π}{6} + 2 πn

Dividir ambos lados entre

2

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

Simplificar

\frac{2 x}{2} \geq \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 las propiedades de las fracciones:

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

= \frac{5 π}{6 \cdot 2}

Multiplicar los numeros:

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 \geq \frac{5 π}{12} + πn

x \geq \frac{5 π}{12} + πn

x \geq \frac{5 π}{12} + πn

2 x \leq 2 π - arccos (- \frac{3}{2}) + 2 πn : x \leq \frac{7 π}{12} + πn

2 x \leq 2 π - arccos (- \frac{3}{2}) + 2 πn

Simplificar

2 π - arccos (- \frac{3}{2}) + 2 πn : 2 π - \frac{5 π}{6} + 2 πn

2 π - arccos (- \frac{3}{2}) + 2 πn

Utilizar la siguiente identidad trivial:

arccos (- \frac{3}{2}) = \frac{5 π}{6}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= 2 π - \frac{5 π}{6} + 2 πn

2 x \leq 2 π - \frac{5 π}{6} + 2 πn

Dividir ambos lados entre

2

2 x \leq 2 π - \frac{5 π}{6} + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} \leq \frac{2 π}{2} - \frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2}

Simplificar

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

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

\frac{2 π}{2} = π

\frac{2 π}{2}

Dividir:

\frac{2}{2} = 1

= π

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

\frac{\frac{5 π}{6}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{5 π}{6 \cdot 2}

Multiplicar los numeros:

6 \cdot 2 = 12

= \frac{5 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= π - \frac{5 π}{12} + πn

x \leq π - \frac{5 π}{12} + πn

x \leq π - \frac{5 π}{12} + πn

Simplificar

π - \frac{5 π}{12} : \frac{7 π}{12}

π - \frac{5 π}{12}

Convertir a fracción:

π = \frac{π 12}{12}

= \frac{π 12}{12} - \frac{5 π}{12}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{π 12 - 5 π}{12}

Sumar elementos similares:

12 π - 5 π = 7 π

= \frac{7 π}{12}

x \leq \frac{7 π}{12} + πn

x \leq \frac{7 π}{12} + πn

Combinar los rangos

x \geq \frac{5 π}{12} + πn and x \leq \frac{7 π}{12} + πn

Mezclar intervalos sobrepuestos

\frac{5 π}{12} + πn \leq x \leq \frac{7 π}{12} + πn

Ejemplos populares

sin(x)>= (sqrt(3))/2

sin (x) \geq \frac{3}{2}

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2cos(x)-1<0

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1250>600cos((2pi)/3 (t-1))+1000

1250 > 600 cos (\frac{2 π}{3} (t - 1)) + 1000

sec(x)<= 2/(sqrt(3))

sec (x) \leq \frac{2}{3}