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Popular Trigonometria >

tan(4x+6)=-0.272

Solução

tan (4 x + 6) = - 0.272

Solução

x = - \frac{3}{2} + \frac{πn}{4} - \frac{0.26557 \dots}{4}

+1

Graus

x = - 89.74775 \dots^{\circ} + 4 5^{\circ} n

Passos da solução

tan (4 x + 6) = - 0.272

Aplique as propriedades trigonométricas inversas

tan (4 x + 6) = - 0.272

Soluções gerais para

tan (4 x + 6) = - 0.272

tan (x) = - a \Rightarrow x = arctan (- a) + πn

4 x + 6 = arctan (- 0.272) + πn

4 x + 6 = arctan (- 0.272) + πn

Resolver

4 x + 6 = arctan (- 0.272) + πn : x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

4 x + 6 = arctan (- 0.272) + πn

Simplificar

arctan (- 0.272) + πn : - arctan (\frac{34}{125}) + πn

arctan (- 0.272) + πn

arctan (- 0.272) = - arctan (\frac{34}{125})

arctan (- 0.272)

= arctan (- \frac{34}{125})

Utilizar a seguinte propriedade:

arctan (- x) = - arctan (x)

arctan (- \frac{34}{125}) = - arctan (\frac{34}{125})

= - arctan (\frac{34}{125})

= - arctan (\frac{34}{125}) + πn

4 x + 6 = - arctan (\frac{34}{125}) + πn

Mova

6

para o lado direito

4 x + 6 = - arctan (\frac{34}{125}) + πn

Subtrair

6

de ambos os lados

4 x + 6 - 6 = - arctan (\frac{34}{125}) + πn - 6

Simplificar

4 x = - arctan (\frac{34}{125}) + πn - 6

4 x = - arctan (\frac{34}{125}) + πn - 6

Dividir ambos os lados por

4

4 x = - arctan (\frac{34}{125}) + πn - 6

Dividir ambos os lados por

4

\frac{4 x}{4} = - \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

Simplificar

\frac{4 x}{4} = - \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

- \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4} : - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

- \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

Agrupar termos semelhantes

= - \frac{6}{4} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

Cancelar

\frac{6}{4} : \frac{3}{2}

\frac{6}{4}

Eliminar o fator comum:

2

= \frac{3}{2}

= - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

Mostrar soluções na forma decimal

x = - \frac{3}{2} + \frac{πn}{4} - \frac{0.26557 \dots}{4}

Gráfico

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