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Popular Trigonometria >

sin^5(3x^2+2)=0.35

Solução

sin^{5} (3 x^{2} + 2) = 0.35

Solução

x = \frac{0.94519 \dots + 2 πn - 2}{3}, x = - \frac{0.94519 \dots + 2 πn - 2}{3}, x = \frac{π - 0.94519 \dots + 2 πn - 2}{3}, x = - \frac{π - 0.94519 \dots + 2 πn - 2}{3}

Graus

x = 0^{\circ} + 75.63899 \dots^{\circ} n, x = 0^{\circ} - 75.63899 \dots^{\circ} n, x = 0^{\circ} + 84.20452 \dots^{\circ} n, x = 0^{\circ} - 84.20452 \dots^{\circ} n

Passos da solução

sin^{5} (3 x^{2} + 2) = 0.35

Para

x^{n} = f (a)

, n é ímpar, a solução é

x = n f (a)

sin (3 x^{2} + 2) = 5 0.35

Aplique as propriedades trigonométricas inversas

sin (3 x^{2} + 2) = 5 0.35

Soluções gerais para

sin (3 x^{2} + 2) = 5 0.35

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn, 3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn, 3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

Resolver

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn : x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn

Mova

2

para o lado direito

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn

Subtrair

2

de ambos os lados

3 x^{2} + 2 - 2 = arcsin (5 0.35) + 2 πn - 2

Simplificar

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

Dividir ambos os lados por

3

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

Dividir ambos os lados por

3

\frac{3 x ^{2}}{3} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Simplificar

x^{2} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

x^{2} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Para

x^{2} = f (a)

as soluções são

x = f (a), - f (a)

x = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}, x = - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Simplificar

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Combinar as frações usando o mínimo múltiplo comum:

\frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Aplicar a regra

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

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Simplificar

- \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

- \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Combinar as frações usando o mínimo múltiplo comum:

\frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Aplicar a regra

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

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= - \frac{2 πn + arcsin ( 5 0.35 ) - 2}{3}

= - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Resolver

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn : x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

Mova

2

para o lado direito

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

Subtrair

2

de ambos os lados

3 x^{2} + 2 - 2 = π - arcsin (5 0.35) + 2 πn - 2

Simplificar

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

Dividir ambos os lados por

3

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

Dividir ambos os lados por

3

\frac{3 x ^{2}}{3} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Simplificar

x^{2} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

x^{2} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Para

x^{2} = f (a)

as soluções são

x = f (a), - f (a)

x = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}, x = - \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Simplificar

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Combinar as frações usando o mínimo múltiplo comum:

\frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Aplicar a regra

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

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Simplificar

- \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

- \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Combinar as frações usando o mínimo múltiplo comum:

\frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Aplicar a regra

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

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= - \frac{π + 2 πn - 2 - arcsin ( 5 0.35 )}{3}

= - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Mostrar soluções na forma decimal

x = \frac{0.94519 \dots + 2 πn - 2}{3}, x = - \frac{0.94519 \dots + 2 πn - 2}{3}, x = \frac{π - 0.94519 \dots + 2 πn - 2}{3}, x = - \frac{π - 0.94519 \dots + 2 πn - 2}{3}

Gráfico

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