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Popular Trigonometría >

10<5sin(pi/6 (x-10))+6

Solución

10 < 5 sin (\frac{π}{6} (x - 10)) + 6

Solución

\frac{6 arcsin ( \frac{4}{5} ) + 10 π}{π} + 12 n < x < \frac{16 π - 6 arcsin ( \frac{4}{5} )}{π} + 12 n

Notación de intervalos

(\frac{6 arcsin ( \frac{4}{5} ) + 10 π}{π} + 12 n, \frac{16 π - 6 arcsin ( \frac{4}{5} )}{π} + 12 n)

Decimal

11.77100 \dots + 12 n < x < 14.22899 \dots + 12 n

Pasos de solución

10 < 5 sin (\frac{π}{6} (x - 10)) + 6

Intercambiar lados

5 sin (\frac{π}{6} (x - 10)) + 6 > 10

Desplace

6

a la derecha

5 sin (\frac{π}{6} (x - 10)) + 6 > 10

Restar

6

de ambos lados

5 sin (\frac{π}{6} (x - 10)) + 6 - 6 > 10 - 6

Simplificar

5 sin (\frac{π}{6} (x - 10)) > 4

5 sin (\frac{π}{6} (x - 10)) > 4

Dividir ambos lados entre

5

5 sin (\frac{π}{6} (x - 10)) > 4

Dividir ambos lados entre

5

\frac{5 sin ( \frac{π}{6} ( x - 10 ) )}{5} > \frac{4}{5}

Simplificar

sin (\frac{π}{6} (x - 10)) > \frac{4}{5}

sin (\frac{π}{6} (x - 10)) > \frac{4}{5}

Para

sin (x) > a

, si

- 1 \leq a < 1

entonces

arcsin (a) + 2 πn < x < π - arcsin (a) + 2 πn

arcsin (\frac{4}{5}) + 2 πn < \frac{π}{6} (x - 10) < π - arcsin (\frac{4}{5}) + 2 πn

a < u < b

entonces

a < u and u < b

arcsin (\frac{4}{5}) + 2 πn < \frac{π}{6} (x - 10) and \frac{π}{6} (x - 10) < π - arcsin (\frac{4}{5}) + 2 πn

arcsin (\frac{4}{5}) + 2 πn < \frac{π}{6} (x - 10) : x > \frac{6 arcsin ( \frac{4}{5} ) + 10 π}{π} + 12 n

arcsin (\frac{4}{5}) + 2 πn < \frac{π}{6} (x - 10)

Intercambiar lados

\frac{π}{6} (x - 10) > arcsin (\frac{4}{5}) + 2 πn

Multiplicar ambos lados por

6

\frac{π}{6} (x - 10) > arcsin (\frac{4}{5}) + 2 πn

Multiplicar ambos lados por

6

6 \cdot \frac{π}{6} (x - 10) > 6 arcsin (\frac{4}{5}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (x - 10) > 6 arcsin (\frac{4}{5}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (x - 10) : π (x - 10)

6 \cdot \frac{π}{6} (x - 10)

Multiplicar fracciones:

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

= \frac{6 π}{6} (x - 10)

Eliminar los terminos comunes:

6

= (x - 10) π

Simplificar

6 arcsin (\frac{4}{5}) + 6 \cdot 2 πn : 6 arcsin (\frac{4}{5}) + 12 πn

6 arcsin (\frac{4}{5}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= 6 arcsin (\frac{4}{5}) + 12 πn

π (x - 10) > 6 arcsin (\frac{4}{5}) + 12 πn

π (x - 10) > 6 arcsin (\frac{4}{5}) + 12 πn

π (x - 10) > 6 arcsin (\frac{4}{5}) + 12 πn

Dividir ambos lados entre

π

π (x - 10) > 6 arcsin (\frac{4}{5}) + 12 πn

Dividir ambos lados entre

π

\frac{π ( x - 10 )}{π} > \frac{6 arcsin ( \frac{4}{5} )}{π} + \frac{12 πn}{π}

Simplificar

x - 10 > \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

x - 10 > \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

Desplace

10

a la derecha

x - 10 > \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

Sumar

10

a ambos lados

x - 10 + 10 > \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n + 10

Simplificar

x > \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n + 10

x > \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n + 10

Simplificar

\frac{6 arcsin ( \frac{4}{5} )}{π} + 10 : \frac{6 arcsin ( \frac{4}{5} ) + 10 π}{π}

\frac{6 arcsin ( \frac{4}{5} )}{π} + 10

Convertir a fracción:

10 = \frac{10 π}{π}

= \frac{6 arcsin ( \frac{4}{5} )}{π} + \frac{10 π}{π}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{6 arcsin ( \frac{4}{5} ) + 10 π}{π}

x > \frac{6 arcsin ( \frac{4}{5} ) + 10 π}{π} + 12 n

\frac{π}{6} (x - 10) < π - arcsin (\frac{4}{5}) + 2 πn : x < \frac{16 π - 6 arcsin ( \frac{4}{5} )}{π} + 12 n

\frac{π}{6} (x - 10) < π - arcsin (\frac{4}{5}) + 2 πn

Multiplicar ambos lados por

6

\frac{π}{6} (x - 10) < π - arcsin (\frac{4}{5}) + 2 πn

Multiplicar ambos lados por

6

6 \cdot \frac{π}{6} (x - 10) < 6 π - 6 arcsin (\frac{4}{5}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (x - 10) < 6 π - 6 arcsin (\frac{4}{5}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (x - 10) : π (x - 10)

6 \cdot \frac{π}{6} (x - 10)

Multiplicar fracciones:

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

= \frac{6 π}{6} (x - 10)

Eliminar los terminos comunes:

6

= (x - 10) π

Simplificar

6 π - 6 arcsin (\frac{4}{5}) + 6 \cdot 2 πn : 6 π - 6 arcsin (\frac{4}{5}) + 12 πn

6 π - 6 arcsin (\frac{4}{5}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= 6 π - 6 arcsin (\frac{4}{5}) + 12 πn

π (x - 10) < 6 π - 6 arcsin (\frac{4}{5}) + 12 πn

π (x - 10) < 6 π - 6 arcsin (\frac{4}{5}) + 12 πn

π (x - 10) < 6 π - 6 arcsin (\frac{4}{5}) + 12 πn

Dividir ambos lados entre

π

π (x - 10) < 6 π - 6 arcsin (\frac{4}{5}) + 12 πn

Dividir ambos lados entre

π

\frac{π ( x - 10 )}{π} < \frac{6 π}{π} - \frac{6 arcsin ( \frac{4}{5} )}{π} + \frac{12 πn}{π}

Simplificar

\frac{π ( x - 10 )}{π} < \frac{6 π}{π} - \frac{6 arcsin ( \frac{4}{5} )}{π} + \frac{12 πn}{π}

Simplificar

\frac{π ( x - 10 )}{π} : x - 10

\frac{π ( x - 10 )}{π}

Eliminar los terminos comunes:

π

= x - 10

Simplificar

\frac{6 π}{π} - \frac{6 arcsin ( \frac{4}{5} )}{π} + \frac{12 πn}{π} : 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

\frac{6 π}{π} - \frac{6 arcsin ( \frac{4}{5} )}{π} + \frac{12 πn}{π}

Cancelar

\frac{6 π}{π} : 6

\frac{6 π}{π}

Eliminar los terminos comunes:

π

= 6

= 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + \frac{12 πn}{π}

Cancelar

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Eliminar los terminos comunes:

π

= 12 n

= 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

x - 10 < 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

x - 10 < 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

x - 10 < 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

Desplace

10

a la derecha

x - 10 < 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n

Sumar

10

a ambos lados

x - 10 + 10 < 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n + 10

Simplificar

x - 10 + 10 < 6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n + 10

Simplificar

x - 10 + 10 : x

x - 10 + 10

Sumar elementos similares:

- 10 + 10 < 0

= x

Simplificar

6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n + 10 : 12 n + 16 - \frac{6 arcsin ( \frac{4}{5} )}{π}

6 - \frac{6 arcsin ( \frac{4}{5} )}{π} + 12 n + 10

Sumar:

6 + 10 = 16

= 12 n + 16 - \frac{6 arcsin ( \frac{4}{5} )}{π}

x < 12 n + 16 - \frac{6 arcsin ( \frac{4}{5} )}{π}

x < 12 n + 16 - \frac{6 arcsin ( \frac{4}{5} )}{π}

x < 12 n + 16 - \frac{6 arcsin ( \frac{4}{5} )}{π}

Simplificar

16 - \frac{6 arcsin ( \frac{4}{5} )}{π} : \frac{16 π - 6 arcsin ( \frac{4}{5} )}{π}

16 - \frac{6 arcsin ( \frac{4}{5} )}{π}

Convertir a fracción:

16 = \frac{16 π}{π}

= \frac{16 π}{π} - \frac{6 arcsin ( \frac{4}{5} )}{π}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{16 π - 6 arcsin ( \frac{4}{5} )}{π}

x < \frac{16 π - 6 arcsin ( \frac{4}{5} )}{π} + 12 n

Combinar los rangos

x > \frac{6 arcsin ( \frac{4}{5} ) + 10 π}{π} + 12 n and x < \frac{16 π - 6 arcsin ( \frac{4}{5} )}{π} + 12 n

Mezclar intervalos sobrepuestos

\frac{6 arcsin ( \frac{4}{5} ) + 10 π}{π} + 12 n < x < \frac{16 π - 6 arcsin ( \frac{4}{5} )}{π} + 12 n

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