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Popular Trigonometria >

sin(pi/2 (x+1))= 2/5

Solução

sin (\frac{π}{2} (x + 1)) = \frac{2}{5}

Solução

x = \frac{2 \cdot 0.41151 \dots}{π} + 4 n - 1, x = 4 n + 1 - \frac{2 \cdot 0.41151 \dots}{π}

Graus

x = - 42.28544 \dots^{\circ} + 229.18311 \dots^{\circ} n, x = 42.28544 \dots^{\circ} + 229.18311 \dots^{\circ} n

Passos da solução

sin (\frac{π}{2} (x + 1)) = \frac{2}{5}

Aplique as propriedades trigonométricas inversas

sin (\frac{π}{2} (x + 1)) = \frac{2}{5}

Soluções gerais para

sin (\frac{π}{2} (x + 1)) = \frac{2}{5}

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

\frac{π}{2} (x + 1) = arcsin (\frac{2}{5}) + 2 πn, \frac{π}{2} (x + 1) = π - arcsin (\frac{2}{5}) + 2 πn

\frac{π}{2} (x + 1) = arcsin (\frac{2}{5}) + 2 πn, \frac{π}{2} (x + 1) = π - arcsin (\frac{2}{5}) + 2 πn

Resolver

\frac{π}{2} (x + 1) = arcsin (\frac{2}{5}) + 2 πn : x = \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1

\frac{π}{2} (x + 1) = arcsin (\frac{2}{5}) + 2 πn

Multiplicar ambos os lados por

2

\frac{π}{2} (x + 1) = arcsin (\frac{2}{5}) + 2 πn

Multiplicar ambos os lados por

2

2 \cdot \frac{π}{2} (x + 1) = 2 arcsin (\frac{2}{5}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{π}{2} (x + 1) = 2 arcsin (\frac{2}{5}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{π}{2} (x + 1) : π (x + 1)

2 \cdot \frac{π}{2} (x + 1)

Multiplicar frações:

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

= \frac{2 π}{2} (x + 1)

Eliminar o fator comum:

2

= (x + 1) π

Simplificar

2 arcsin (\frac{2}{5}) + 2 \cdot 2 πn : 2 arcsin (\frac{2}{5}) + 4 πn

2 arcsin (\frac{2}{5}) + 2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 2 arcsin (\frac{2}{5}) + 4 πn

π (x + 1) = 2 arcsin (\frac{2}{5}) + 4 πn

π (x + 1) = 2 arcsin (\frac{2}{5}) + 4 πn

π (x + 1) = 2 arcsin (\frac{2}{5}) + 4 πn

Dividir ambos os lados por

π

π (x + 1) = 2 arcsin (\frac{2}{5}) + 4 πn

Dividir ambos os lados por

π

\frac{π ( x + 1 )}{π} = \frac{2 arcsin ( \frac{2}{5} )}{π} + \frac{4 πn}{π}

Simplificar

x + 1 = \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

x + 1 = \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

Mova

1

para o lado direito

x + 1 = \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

Subtrair

1

de ambos os lados

x + 1 - 1 = \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1

Simplificar

x = \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1

x = \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1

Resolver

\frac{π}{2} (x + 1) = π - arcsin (\frac{2}{5}) + 2 πn : x = 4 n + 1 - \frac{2 arcsin ( \frac{2}{5} )}{π}

\frac{π}{2} (x + 1) = π - arcsin (\frac{2}{5}) + 2 πn

Multiplicar ambos os lados por

2

\frac{π}{2} (x + 1) = π - arcsin (\frac{2}{5}) + 2 πn

Multiplicar ambos os lados por

2

2 \cdot \frac{π}{2} (x + 1) = 2 π - 2 arcsin (\frac{2}{5}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{π}{2} (x + 1) = 2 π - 2 arcsin (\frac{2}{5}) + 2 \cdot 2 πn

Simplificar

2 \cdot \frac{π}{2} (x + 1) : π (x + 1)

2 \cdot \frac{π}{2} (x + 1)

Multiplicar frações:

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

= \frac{2 π}{2} (x + 1)

Eliminar o fator comum:

2

= (x + 1) π

Simplificar

2 π - 2 arcsin (\frac{2}{5}) + 2 \cdot 2 πn : 2 π - 2 arcsin (\frac{2}{5}) + 4 πn

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

Multiplicar os números:

2 \cdot 2 = 4

= 2 π - 2 arcsin (\frac{2}{5}) + 4 πn

π (x + 1) = 2 π - 2 arcsin (\frac{2}{5}) + 4 πn

π (x + 1) = 2 π - 2 arcsin (\frac{2}{5}) + 4 πn

π (x + 1) = 2 π - 2 arcsin (\frac{2}{5}) + 4 πn

Dividir ambos os lados por

π

π (x + 1) = 2 π - 2 arcsin (\frac{2}{5}) + 4 πn

Dividir ambos os lados por

π

\frac{π ( x + 1 )}{π} = \frac{2 π}{π} - \frac{2 arcsin ( \frac{2}{5} )}{π} + \frac{4 πn}{π}

Simplificar

\frac{π ( x + 1 )}{π} = \frac{2 π}{π} - \frac{2 arcsin ( \frac{2}{5} )}{π} + \frac{4 πn}{π}

Simplificar

\frac{π ( x + 1 )}{π} : x + 1

\frac{π ( x + 1 )}{π}

Eliminar o fator comum:

π

= x + 1

Simplificar

\frac{2 π}{π} - \frac{2 arcsin ( \frac{2}{5} )}{π} + \frac{4 πn}{π} : 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

\frac{2 π}{π} - \frac{2 arcsin ( \frac{2}{5} )}{π} + \frac{4 πn}{π}

Cancelar

\frac{2 π}{π} : 2

\frac{2 π}{π}

Eliminar o fator comum:

π

= 2

= 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + \frac{4 πn}{π}

Cancelar

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

Eliminar o fator comum:

π

= 4 n

= 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

x + 1 = 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

x + 1 = 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

x + 1 = 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

Mova

1

para o lado direito

x + 1 = 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n

Subtrair

1

de ambos os lados

x + 1 - 1 = 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1

Simplificar

x + 1 - 1 = 2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1

Simplificar

x + 1 - 1 : x

x + 1 - 1

Somar elementos similares:

1 - 1 = 0

= x

Simplificar

2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1 : 4 n + 1 - \frac{2 arcsin ( \frac{2}{5} )}{π}

2 - \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1

Subtrair:

2 - 1 = 1

= 4 n + 1 - \frac{2 arcsin ( \frac{2}{5} )}{π}

x = 4 n + 1 - \frac{2 arcsin ( \frac{2}{5} )}{π}

x = 4 n + 1 - \frac{2 arcsin ( \frac{2}{5} )}{π}

x = 4 n + 1 - \frac{2 arcsin ( \frac{2}{5} )}{π}

x = \frac{2 arcsin ( \frac{2}{5} )}{π} + 4 n - 1, x = 4 n + 1 - \frac{2 arcsin ( \frac{2}{5} )}{π}

Mostrar soluções na forma decimal

x = \frac{2 \cdot 0.41151 \dots}{π} + 4 n - 1, x = 4 n + 1 - \frac{2 \cdot 0.41151 \dots}{π}

Gráfico

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