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Popular Trigonometria >

-cos(3x)<0

Solução

- cos (3 x) < 0

Solução

- \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{6} + \frac{2 π}{3} n

Notação de intervalo

(- \frac{π}{6} + \frac{2 π}{3} n, \frac{π}{6} + \frac{2 π}{3} n)

Decimal

- 0.52359 \dots + \frac{2 π}{3} n < x < 0.52359 \dots + \frac{2 π}{3} n

Passos da solução

- cos (3 x) < 0

Multiplicar ambos os lados por

- 1

- cos (3 x) < 0

Multiplicar ambos os lados por -1 (inverte a desigualdade)

(- cos (3 x)) (- 1) > 0 \cdot (- 1)

Simplificar

cos (3 x) > 0

cos (3 x) > 0

Para

cos (x) > a

, se

- 1 \leq a < 1

então

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

- arccos (0) + 2 πn < 3 x < arccos (0) + 2 πn

a < u < b

então

a < u and u < b

- arccos (0) + 2 πn < 3 x and 3 x < arccos (0) + 2 πn

- arccos (0) + 2 πn < 3 x : x > - \frac{π}{6} + \frac{2 πn}{3}

- arccos (0) + 2 πn < 3 x

Trocar lados

3 x > - arccos (0) + 2 πn

Simplificar

- arccos (0) + 2 πn : - \frac{π}{2} + 2 πn

- arccos (0) + 2 πn

Utilizar a seguinte identidade trivial:

arccos (0) = \frac{π}{2}

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}{2} + 2 πn

3 x > - \frac{π}{2} + 2 πn

Dividir ambos os lados por

3

3 x > - \frac{π}{2} + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} > - \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} > - \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

- \frac{\frac{π}{2}}{3} + \frac{2 πn}{3} : - \frac{π}{6} + \frac{2 πn}{3}

- \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} = \frac{π}{6}

\frac{\frac{π}{2}}{3}

Aplicar as propriedades das frações:

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

= \frac{π}{2 \cdot 3}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{π}{6}

= - \frac{π}{6} + \frac{2 πn}{3}

x > - \frac{π}{6} + \frac{2 πn}{3}

x > - \frac{π}{6} + \frac{2 πn}{3}

x > - \frac{π}{6} + \frac{2 πn}{3}

3 x < arccos (0) + 2 πn : x < \frac{π}{6} + \frac{2 πn}{3}

3 x < arccos (0) + 2 πn

Simplificar

arccos (0) + 2 πn : \frac{π}{2} + 2 πn

arccos (0) + 2 πn

Utilizar a seguinte identidade trivial:

arccos (0) = \frac{π}{2}

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}{2} + 2 πn

3 x < \frac{π}{2} + 2 πn

Dividir ambos os lados por

3

3 x < \frac{π}{2} + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} < \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} < \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3} : \frac{π}{6} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} = \frac{π}{6}

\frac{\frac{π}{2}}{3}

Aplicar as propriedades das frações:

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

= \frac{π}{2 \cdot 3}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{2 πn}{3}

x < \frac{π}{6} + \frac{2 πn}{3}

x < \frac{π}{6} + \frac{2 πn}{3}

x < \frac{π}{6} + \frac{2 πn}{3}

Combinar os intervalos

x > - \frac{π}{6} + \frac{2 πn}{3} and x < \frac{π}{6} + \frac{2 πn}{3}

Junte intervalos que se sobrepoem

- \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{6} + \frac{2 π}{3} n

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sin (x) + \frac{1}{2} > 0

tan(x)<=-3

tan (x) \leq - 3

1/4 sin(x)>=-1

\frac{1}{4} sin (x) \geq - 1