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Popular Trigonometria >

0.16085=sin((2pi)/(365)(x-114))

Solução

0.16085 = sin (\frac{2 π}{365} (x - 114))

Solução

x = \frac{365 \cdot 0.16155 \dots}{2 π} + 365 n + 114, x = 365 n + \frac{593}{2} - \frac{365 \cdot 0.16155 \dots}{2 π}

Graus

x = 7069.42804 \dots^{\circ} + 20912.95952 \dots^{\circ} n, x = 16450.48944 \dots^{\circ} + 20912.95952 \dots^{\circ} n

Passos da solução

0.16085 = sin (\frac{2 π}{365} (x - 114))

Trocar lados

sin (\frac{2 π}{365} (x - 114)) = 0.16085

Aplique as propriedades trigonométricas inversas

sin (\frac{2 π}{365} (x - 114)) = 0.16085

Soluções gerais para

sin (\frac{2 π}{365} (x - 114)) = 0.16085

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

\frac{2 π}{365} (x - 114) = arcsin (0.16085) + 2 πn, \frac{2 π}{365} (x - 114) = π - arcsin (0.16085) + 2 πn

\frac{2 π}{365} (x - 114) = arcsin (0.16085) + 2 πn, \frac{2 π}{365} (x - 114) = π - arcsin (0.16085) + 2 πn

Resolver

\frac{2 π}{365} (x - 114) = arcsin (0.16085) + 2 πn : x = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114

\frac{2 π}{365} (x - 114) = arcsin (0.16085) + 2 πn

Multiplicar ambos os lados por

365

\frac{2 π}{365} (x - 114) = arcsin (0.16085) + 2 πn

Multiplicar ambos os lados por

365

365 \cdot \frac{2 π}{365} (x - 114) = 365 arcsin (0.16085) + 365 \cdot 2 πn

Simplificar

2 π (x - 114) = 365 arcsin (0.16085) + 730 πn

2 π (x - 114) = 365 arcsin (0.16085) + 730 πn

Dividir ambos os lados por

2 π

2 π (x - 114) = 365 arcsin (0.16085) + 730 πn

Dividir ambos os lados por

2 π

\frac{2 π ( x - 114 )}{2 π} = \frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x - 114 )}{2 π} = \frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x - 114 )}{2 π} : x - 114

\frac{2 π ( x - 114 )}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π ( x - 114 )}{π}

Eliminar o fator comum:

π

= x - 114

Simplificar

\frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π} : \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

\frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π}

Cancelar

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

Cancelar

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

Dividir:

\frac{730}{2} = 365

= \frac{365 πn}{π}

Eliminar o fator comum:

π

= 365 n

= 365 n

= \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

x - 114 = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

x - 114 = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

x - 114 = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

Mova

114

para o lado direito

x - 114 = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

Adicionar

114

a ambos os lados

x - 114 + 114 = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114

Simplificar

x = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114

x = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114

Resolver

\frac{2 π}{365} (x - 114) = π - arcsin (0.16085) + 2 πn : x = 365 n + \frac{593}{2} - \frac{365 arcsin ( 0.16085 )}{2 π}

\frac{2 π}{365} (x - 114) = π - arcsin (0.16085) + 2 πn

Multiplicar ambos os lados por

365

\frac{2 π}{365} (x - 114) = π - arcsin (0.16085) + 2 πn

Multiplicar ambos os lados por

365

365 \cdot \frac{2 π}{365} (x - 114) = 365 π - 365 arcsin (0.16085) + 365 \cdot 2 πn

Simplificar

2 π (x - 114) = 365 π - 365 arcsin (0.16085) + 730 πn

2 π (x - 114) = 365 π - 365 arcsin (0.16085) + 730 πn

Dividir ambos os lados por

2 π

2 π (x - 114) = 365 π - 365 arcsin (0.16085) + 730 πn

Dividir ambos os lados por

2 π

\frac{2 π ( x - 114 )}{2 π} = \frac{365 π}{2 π} - \frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x - 114 )}{2 π} = \frac{365 π}{2 π} - \frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x - 114 )}{2 π} : x - 114

\frac{2 π ( x - 114 )}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π ( x - 114 )}{π}

Eliminar o fator comum:

π

= x - 114

Simplificar

\frac{365 π}{2 π} - \frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π} : \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

\frac{365 π}{2 π} - \frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π}

Cancelar

\frac{365 π}{2 π} : \frac{365}{2}

\frac{365 π}{2 π}

Eliminar o fator comum:

π

= \frac{365}{2}

= \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + \frac{730 πn}{2 π}

Cancelar

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

Cancelar

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

Dividir:

\frac{730}{2} = 365

= \frac{365 πn}{π}

Eliminar o fator comum:

π

= 365 n

= 365 n

= \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

x - 114 = \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

x - 114 = \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

x - 114 = \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

Mova

114

para o lado direito

x - 114 = \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n

Adicionar

114

a ambos os lados

x - 114 + 114 = \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114

Simplificar

x - 114 + 114 = \frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114

Simplificar

x - 114 + 114 : x

x - 114 + 114

Somar elementos similares:

- 114 + 114 = 0

= x

Simplificar

\frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114 : 365 n + \frac{593}{2} - \frac{365 arcsin ( 0.16085 )}{2 π}

\frac{365}{2} - \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114

Combinar as frações usando o mínimo múltiplo comum:

\frac{593}{2}

114 + \frac{365}{2}

Converter para fração:

114 = \frac{114 \cdot 2}{2}

= \frac{114 \cdot 2}{2} + \frac{365}{2}

Já que os denominadores são iguais, combinar as frações:

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

= \frac{114 \cdot 2 + 365}{2}

114 \cdot 2 + 365 = 593

114 \cdot 2 + 365

Multiplicar os números:

114 \cdot 2 = 228

= 228 + 365

Somar:

228 + 365 = 593

= 593

= \frac{593}{2}

= 365 n + \frac{593}{2} - \frac{365 arcsin ( 0.16085 )}{2 π}

x = 365 n + \frac{593}{2} - \frac{365 arcsin ( 0.16085 )}{2 π}

x = 365 n + \frac{593}{2} - \frac{365 arcsin ( 0.16085 )}{2 π}

x = 365 n + \frac{593}{2} - \frac{365 arcsin ( 0.16085 )}{2 π}

x = \frac{365 arcsin ( 0.16085 )}{2 π} + 365 n + 114, x = 365 n + \frac{593}{2} - \frac{365 arcsin ( 0.16085 )}{2 π}

Mostrar soluções na forma decimal

x = \frac{365 \cdot 0.16155 \dots}{2 π} + 365 n + 114, x = 365 n + \frac{593}{2} - \frac{365 \cdot 0.16155 \dots}{2 π}

Gráfico

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