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Popular Trigonometría >

3cos(2x)+2< 5/2

Solución

3 cos (2 x) + 2 < \frac{5}{2}

Solución

\frac{arccos ( \frac{1}{6} )}{2} + πn < x < \frac{2 π - arccos ( \frac{1}{6} )}{2} + πn

Notación de intervalos

(\frac{arccos ( \frac{1}{6} )}{2} + πn, \frac{2 π - arccos ( \frac{1}{6} )}{2} + πn)

Decimal

0.70167 \dots + πn < x < 2.43991 \dots + πn

Pasos de solución

3 cos (2 x) + 2 < \frac{5}{2}

Desplace

2

a la derecha

3 cos (2 x) + 2 < \frac{5}{2}

Restar

2

de ambos lados

3 cos (2 x) + 2 - 2 < \frac{5}{2} - 2

Simplificar

3 cos (2 x) + 2 - 2 < \frac{5}{2} - 2

Simplificar

3 cos (2 x) + 2 - 2 : 3 cos (2 x)

3 cos (2 x) + 2 - 2

Sumar elementos similares:

2 - 2 < 0

= 3 cos (2 x)

Simplificar

\frac{5}{2} - 2 : \frac{1}{2}

\frac{5}{2} - 2

Convertir a fracción:

2 = \frac{2 \cdot 2}{2}

= - \frac{2 \cdot 2}{2} + \frac{5}{2}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{- 2 \cdot 2 + 5}{2}

- 2 \cdot 2 + 5 = 1

- 2 \cdot 2 + 5

Multiplicar los numeros:

2 \cdot 2 = 4

= - 4 + 5

Sumar/restar lo siguiente:

- 4 + 5 = 1

= 1

= \frac{1}{2}

3 cos (2 x) < \frac{1}{2}

3 cos (2 x) < \frac{1}{2}

3 cos (2 x) < \frac{1}{2}

Dividir ambos lados entre

3

3 cos (2 x) < \frac{1}{2}

Dividir ambos lados entre

3

\frac{3 cos ( 2 x )}{3} < \frac{\frac{1}{2}}{3}

Simplificar

\frac{3 cos ( 2 x )}{3} < \frac{\frac{1}{2}}{3}

Simplificar

\frac{3 cos ( 2 x )}{3} : cos (2 x)

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

Dividir:

\frac{3}{3} = 1

= cos (2 x)

Simplificar

\frac{\frac{1}{2}}{3} : \frac{1}{6}

\frac{\frac{1}{2}}{3}

Aplicar las propiedades de las fracciones:

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

= \frac{1}{2 \cdot 3}

Multiplicar los numeros:

2 \cdot 3 = 6

= \frac{1}{6}

cos (2 x) < \frac{1}{6}

cos (2 x) < \frac{1}{6}

cos (2 x) < \frac{1}{6}

Para

cos (x) < a

, si

- 1 < a \leq 1

entonces

arccos (a) + 2 πn < x < 2 π - arccos (a) + 2 πn

arccos (\frac{1}{6}) + 2 πn < 2 x < 2 π - arccos (\frac{1}{6}) + 2 πn

a < u < b

entonces

a < u and u < b

arccos (\frac{1}{6}) + 2 πn < 2 x and 2 x < 2 π - arccos (\frac{1}{6}) + 2 πn

arccos (\frac{1}{6}) + 2 πn < 2 x : x > \frac{arccos ( \frac{1}{6} )}{2} + πn

arccos (\frac{1}{6}) + 2 πn < 2 x

Intercambiar lados

2 x > arccos (\frac{1}{6}) + 2 πn

Dividir ambos lados entre

2

2 x > arccos (\frac{1}{6}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} > \frac{arccos ( \frac{1}{6} )}{2} + \frac{2 πn}{2}

Simplificar

x > \frac{arccos ( \frac{1}{6} )}{2} + πn

x > \frac{arccos ( \frac{1}{6} )}{2} + πn

2 x < 2 π - arccos (\frac{1}{6}) + 2 πn : x < \frac{2 π - arccos ( \frac{1}{6} )}{2} + πn

2 x < 2 π - arccos (\frac{1}{6}) + 2 πn

Dividir ambos lados entre

2

2 x < 2 π - arccos (\frac{1}{6}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} < \frac{2 π}{2} - \frac{arccos ( \frac{1}{6} )}{2} + \frac{2 πn}{2}

Simplificar

x < π - \frac{arccos ( \frac{1}{6} )}{2} + πn

Simplificar

π - \frac{arccos ( \frac{1}{6} )}{2} : \frac{2 π - arccos ( \frac{1}{6} )}{2}

π - \frac{arccos ( \frac{1}{6} )}{2}

Convertir a fracción:

π = \frac{π 2}{2}

= \frac{π 2}{2} - \frac{arccos ( \frac{1}{6} )}{2}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{π 2 - arccos ( \frac{1}{6} )}{2}

x < \frac{2 π - arccos ( \frac{1}{6} )}{2} + πn

x < \frac{2 π - arccos ( \frac{1}{6} )}{2} + πn

Combinar los rangos

x > \frac{arccos ( \frac{1}{6} )}{2} + πn and x < \frac{2 π - arccos ( \frac{1}{6} )}{2} + πn

Mezclar intervalos sobrepuestos

\frac{arccos ( \frac{1}{6} )}{2} + πn < x < \frac{2 π - arccos ( \frac{1}{6} )}{2} + πn

Ejemplos populares

sin(x)>-1,0<= x<= 2pi