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Popular Trigonometria >

tan(2x)<3

Solução

tan (2 x) < 3

Solução

- \frac{π}{4} + \frac{π}{2} n < x < \frac{arctan ( 3 )}{2} + \frac{π}{2} n

+2

Notação de intervalo

(- \frac{π}{4} + \frac{π}{2} n, \frac{arctan ( 3 )}{2} + \frac{π}{2} n)

Decimal

- 0.78539 \dots + \frac{π}{2} n < x < 0.62452 \dots + \frac{π}{2} n

Passos da solução

tan (2 x) < 3

Se

tan (x) < a

então

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

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

Se

a < u < b

então

a < u and u < b

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

- \frac{π}{2} + πn < 2 x : x > - \frac{π}{4} + \frac{πn}{2}

- \frac{π}{2} + πn < 2 x

Trocar lados

2 x > - \frac{π}{2} + πn

Dividir ambos os lados por

2

2 x > - \frac{π}{2} + πn

Dividir ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

- \frac{\frac{π}{2}}{2} + \frac{πn}{2} : - \frac{π}{4} + \frac{πn}{2}

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

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Aplicar as propriedades das frações:

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

= \frac{π}{2 \cdot 2}

Multiplicar os números:

2 \cdot 2 = 4

= \frac{π}{4}

= - \frac{π}{4} + \frac{πn}{2}

x > - \frac{π}{4} + \frac{πn}{2}

x > - \frac{π}{4} + \frac{πn}{2}

x > - \frac{π}{4} + \frac{πn}{2}

2 x < arctan (3) + πn : x < \frac{arctan ( 3 )}{2} + \frac{πn}{2}

2 x < arctan (3) + πn

Dividir ambos os lados por

2

2 x < arctan (3) + πn

Dividir ambos os lados por

2

\frac{2 x}{2} < \frac{arctan ( 3 )}{2} + \frac{πn}{2}

Simplificar

x < \frac{arctan ( 3 )}{2} + \frac{πn}{2}

x < \frac{arctan ( 3 )}{2} + \frac{πn}{2}

Combinar os intervalos

x > - \frac{π}{4} + \frac{πn}{2} and x < \frac{arctan ( 3 )}{2} + \frac{πn}{2}

Junte intervalos que se sobrepoem

- \frac{π}{4} + \frac{π}{2} n < x < \frac{arctan ( 3 )}{2} + \frac{π}{2} n

Exemplos populares

cos^2(x)-cos(x)>0

cos^{2} (x) - cos (x) > 0

sin (x) < - 0.5

cos^{2} (x) > 14

cos (y) \geq - 1

3cos(3 x/2-pi/4)-1>0

3 cos (3 \frac{x}{2} - \frac{π}{4}) - 1 > 0