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Popular Trigonometria >

cot((3x)/2)+sqrt(3)<= 0

Solução

cot (\frac{3 x}{2}) + 3 \leq 0

Solução

\frac{5 π}{9} + \frac{2 π}{3} n \leq x < \frac{2 π}{3} + \frac{2 π}{3} n

Notação de intervalo

[\frac{5 π}{9} + \frac{2 π}{3} n, \frac{2 π}{3} + \frac{2 π}{3} n)

Decimal

1.74532 \dots + \frac{2 π}{3} n \leq x < 2.09439 \dots + \frac{2 π}{3} n

Passos da solução

cot (\frac{3 x}{2}) + 3 \leq 0

Mova

3

para o lado direito

cot (\frac{3 x}{2}) + 3 \leq 0

Subtrair

3

de ambos os lados

cot (\frac{3 x}{2}) + 3 - 3 \leq 0 - 3

Simplificar

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

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

cot (x) \leq a

então

arccot (a) + πn \leq x < π + πn

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

a \leq u < b

então

a \leq u and u < b

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

arccot (- 3) + πn \leq \frac{3 x}{2} : x \geq \frac{5 π}{9} + \frac{2 πn}{3}

arccot (- 3) + πn \leq \frac{3 x}{2}

Trocar lados

\frac{3 x}{2} \geq arccot (- 3) + πn

Simplificar

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

arccot (- 3) + πn

Utilizar a seguinte identidade trivial:

arccot (- 3) = \frac{5 π}{6}

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

= \frac{5 π}{6} + πn

\frac{3 x}{2} \geq \frac{5 π}{6} + πn

Multiplicar ambos os lados por

2

\frac{3 x}{2} \geq \frac{5 π}{6} + πn

Multiplicar ambos os lados por

2

\frac{2 \cdot 3 x}{2} \geq 2 \cdot \frac{5 π}{6} + 2 πn

Simplificar

\frac{2 \cdot 3 x}{2} \geq 2 \cdot \frac{5 π}{6} + 2 πn

Simplificar

\frac{2 \cdot 3 x}{2} : 3 x

\frac{2 \cdot 3 x}{2}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{6 x}{2}

Dividir:

\frac{6}{2} = 3

= 3 x

Simplificar

2 \cdot \frac{5 π}{6} + 2 πn : \frac{5 π}{3} + 2 πn

2 \cdot \frac{5 π}{6} + 2 πn

2 \cdot \frac{5 π}{6} = \frac{5 π}{3}

2 \cdot \frac{5 π}{6}

Multiplicar frações:

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

= \frac{5 π 2}{6}

Multiplicar os números:

5 \cdot 2 = 10

= \frac{10 π}{6}

Eliminar o fator comum:

2

= \frac{5 π}{3}

= \frac{5 π}{3} + 2 πn

3 x \geq \frac{5 π}{3} + 2 πn

3 x \geq \frac{5 π}{3} + 2 πn

3 x \geq \frac{5 π}{3} + 2 πn

Dividir ambos os lados por

3

3 x \geq \frac{5 π}{3} + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} \geq \frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} \geq \frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3} : \frac{5 π}{9} + \frac{2 πn}{3}

\frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3}

\frac{\frac{5 π}{3}}{3} = \frac{5 π}{9}

\frac{\frac{5 π}{3}}{3}

Aplicar as propriedades das frações:

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

= \frac{5 π}{3 \cdot 3}

Multiplicar os números:

3 \cdot 3 = 9

= \frac{5 π}{9}

= \frac{5 π}{9} + \frac{2 πn}{3}

x \geq \frac{5 π}{9} + \frac{2 πn}{3}

x \geq \frac{5 π}{9} + \frac{2 πn}{3}

x \geq \frac{5 π}{9} + \frac{2 πn}{3}

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

\frac{3 x}{2} < π + πn

Multiplicar ambos os lados por

2

\frac{3 x}{2} < π + πn

Multiplicar ambos os lados por

2

\frac{2 \cdot 3 x}{2} < 2 π + 2 πn

Simplificar

3 x < 2 π + 2 πn

3 x < 2 π + 2 πn

Dividir ambos os lados por

3

3 x < 2 π + 2 πn

Dividir ambos os lados por

3

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

Simplificar

x < \frac{2 π}{3} + \frac{2 πn}{3}

x < \frac{2 π}{3} + \frac{2 πn}{3}

Combinar os intervalos

x \geq \frac{5 π}{9} + \frac{2 πn}{3} and x < \frac{2 π}{3} + \frac{2 πn}{3}

Junte intervalos que se sobrepoem

\frac{5 π}{9} + \frac{2 π}{3} n \leq x < \frac{2 π}{3} + \frac{2 π}{3} n

Exemplos populares

csc(x)>1

csc (x) > 1

1/(sin^2(x))-1/(cos^2(x))>= 8/3

\frac{1}{sin ^{2} ( x )} - \frac{1}{cos ^{2} ( x )} \geq \frac{8}{3}

cos(x)>= sin(x)

cos (x) \geq sin (x)

sin(x)<1

sin (x) < 1

tan(x)<0.7

tan (x) < 0.7