English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x)< 1/(sqrt(2))

Solución

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

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

Notación de intervalos

(\frac{π}{4} + 2 πn, \frac{7 π}{4} + 2 πn)

Notación decimal

0.78539 \dots + 2 πn < x < 5.49778 \dots + 2 πn

Pasos de solución

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

Simplificar

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

Multiplicar por el conjugado

\frac{2}{2}

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

1 \cdot 2 = 2

22 = 2

22

Aplicar las leyes de los exponentes:

a a = a

22 = 2

= 2

= \frac{2}{2}

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

Para

cos (x) < a

, si

- 1 < a \leq 1

entonces

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

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

Simplificar

arccos (\frac{2}{2}) : \frac{π}{4}

arccos (\frac{2}{2})

Utilizar la siguiente identidad trivial:

arccos (\frac{2}{2}) = \frac{π}{4}

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{π}{4}

Simplificar

2 π - arccos (\frac{2}{2}) : \frac{7 π}{4}

2 π - arccos (\frac{2}{2})

Utilizar la siguiente identidad trivial:

arccos (\frac{2}{2}) = \frac{π}{4}

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{π}{4}

Simplificar

2 π - \frac{π}{4}

Convertir a fracción:

2 π = \frac{2 π 4}{4}

= \frac{2 π 4}{4} - \frac{π}{4}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{2 π 4 - π}{4}

2 π 4 - π = 7 π

2 π 4 - π

Multiplicar los numeros:

2 \cdot 4 = 8

= 8 π - π

Sumar elementos similares:

8 π - π = 7 π

= 7 π

= \frac{7 π}{4}

= \frac{7 π}{4}

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

2 cos^{2} (x) \geq 1.5

cos^{2} (x) - sin^{2} (x) + 3 cos (x) - 2 \leq 0

sin^{2} (x) < \frac{3}{4}

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

tan (x) > \frac{3}{3}