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Popular Trigonometría >

7.5cos(pi/6 (x+3))+10.5>13.75

Solución

7.5 cos (\frac{π}{6} (x + 3)) + 10.5 > 13.75

Solución

\frac{- 6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n < x < \frac{6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n

Notación de intervalos

(\frac{- 6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n, \frac{6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n)

Decimal

- 5.14402 \dots + 12 n < x < - 0.85597 \dots + 12 n

Pasos de solución

7.5 cos (\frac{π}{6} (x + 3)) + 10.5 > 13.75

Multiplicar ambos lados por

100

7.5 cos (\frac{π}{6} (x + 3)) + 10.5 > 13.75

Para eliminar los puntos decimales, multiplique por 10 por cada digito después del punto decimalHay digitos

2

a la derecha del punto decimal, por lo que debe multiplicar por

100

7.5 cos (\frac{π}{6} (x + 3)) \cdot 100 + 10.5 \cdot 100 > 13.75 \cdot 100

Simplificar

750 cos (\frac{π}{6} (x + 3)) + 1050 > 1375

750 cos (\frac{π}{6} (x + 3)) + 1050 > 1375

Desplace

1050

a la derecha

750 cos (\frac{π}{6} (x + 3)) + 1050 > 1375

Restar

1050

de ambos lados

750 cos (\frac{π}{6} (x + 3)) + 1050 - 1050 > 1375 - 1050

Simplificar

750 cos (\frac{π}{6} (x + 3)) > 325

750 cos (\frac{π}{6} (x + 3)) > 325

Dividir ambos lados entre

750

750 cos (\frac{π}{6} (x + 3)) > 325

Dividir ambos lados entre

750

\frac{750 cos ( \frac{π}{6} ( x + 3 ) )}{750} > \frac{325}{750}

Simplificar

cos (\frac{π}{6} (x + 3)) > \frac{13}{30}

cos (\frac{π}{6} (x + 3)) > \frac{13}{30}

Para

cos (x) > a

, si

- 1 \leq a < 1

entonces

- arccos (a) + 2 πn < x < arccos (a) + 2 πn

- arccos (\frac{13}{30}) + 2 πn < \frac{π}{6} (x + 3) < arccos (\frac{13}{30}) + 2 πn

a < u < b

entonces

a < u and u < b

- arccos (\frac{13}{30}) + 2 πn < \frac{π}{6} (x + 3) and \frac{π}{6} (x + 3) < arccos (\frac{13}{30}) + 2 πn

- arccos (\frac{13}{30}) + 2 πn < \frac{π}{6} (x + 3) : x > \frac{- 6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n

- arccos (\frac{13}{30}) + 2 πn < \frac{π}{6} (x + 3)

Intercambiar lados

\frac{π}{6} (x + 3) > - arccos (\frac{13}{30}) + 2 πn

Multiplicar ambos lados por

6

\frac{π}{6} (x + 3) > - arccos (\frac{13}{30}) + 2 πn

Multiplicar ambos lados por

6

6 \cdot \frac{π}{6} (x + 3) > - 6 arccos (\frac{13}{30}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (x + 3) > - 6 arccos (\frac{13}{30}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (x + 3) : π (x + 3)

6 \cdot \frac{π}{6} (x + 3)

Multiplicar fracciones:

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

= \frac{6 π}{6} (x + 3)

Eliminar los terminos comunes:

6

= (x + 3) π

Simplificar

- 6 arccos (\frac{13}{30}) + 6 \cdot 2 πn : - 6 arccos (\frac{13}{30}) + 12 πn

- 6 arccos (\frac{13}{30}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= - 6 arccos (\frac{13}{30}) + 12 πn

π (x + 3) > - 6 arccos (\frac{13}{30}) + 12 πn

π (x + 3) > - 6 arccos (\frac{13}{30}) + 12 πn

π (x + 3) > - 6 arccos (\frac{13}{30}) + 12 πn

Dividir ambos lados entre

π

π (x + 3) > - 6 arccos (\frac{13}{30}) + 12 πn

Dividir ambos lados entre

π

\frac{π ( x + 3 )}{π} > - \frac{6 arccos ( \frac{13}{30} )}{π} + \frac{12 πn}{π}

Simplificar

x + 3 > - \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n

x + 3 > - \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n

Desplace

3

a la derecha

x + 3 > - \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n

Restar

3

de ambos lados

x + 3 - 3 > - \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n - 3

Simplificar

x > - \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n - 3

x > - \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n - 3

Simplificar

- \frac{6 arccos ( \frac{13}{30} )}{π} - 3 : \frac{- 6 arccos ( \frac{13}{30} ) - 3 π}{π}

- \frac{6 arccos ( \frac{13}{30} )}{π} - 3

Convertir a fracción:

3 = \frac{3 π}{π}

= - \frac{6 arccos ( \frac{13}{30} )}{π} - \frac{3 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 arccos ( \frac{13}{30} ) - 3 π}{π}

x > \frac{- 6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n

\frac{π}{6} (x + 3) < arccos (\frac{13}{30}) + 2 πn : x < \frac{6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n

\frac{π}{6} (x + 3) < arccos (\frac{13}{30}) + 2 πn

Multiplicar ambos lados por

6

\frac{π}{6} (x + 3) < arccos (\frac{13}{30}) + 2 πn

Multiplicar ambos lados por

6

6 \cdot \frac{π}{6} (x + 3) < 6 arccos (\frac{13}{30}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (x + 3) < 6 arccos (\frac{13}{30}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (x + 3) : π (x + 3)

6 \cdot \frac{π}{6} (x + 3)

Multiplicar fracciones:

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

= \frac{6 π}{6} (x + 3)

Eliminar los terminos comunes:

6

= (x + 3) π

Simplificar

6 arccos (\frac{13}{30}) + 6 \cdot 2 πn : 6 arccos (\frac{13}{30}) + 12 πn

6 arccos (\frac{13}{30}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= 6 arccos (\frac{13}{30}) + 12 πn

π (x + 3) < 6 arccos (\frac{13}{30}) + 12 πn

π (x + 3) < 6 arccos (\frac{13}{30}) + 12 πn

π (x + 3) < 6 arccos (\frac{13}{30}) + 12 πn

Dividir ambos lados entre

π

π (x + 3) < 6 arccos (\frac{13}{30}) + 12 πn

Dividir ambos lados entre

π

\frac{π ( x + 3 )}{π} < \frac{6 arccos ( \frac{13}{30} )}{π} + \frac{12 πn}{π}

Simplificar

x + 3 < \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n

x + 3 < \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n

Desplace

3

a la derecha

x + 3 < \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n

Restar

3

de ambos lados

x + 3 - 3 < \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n - 3

Simplificar

x < \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n - 3

x < \frac{6 arccos ( \frac{13}{30} )}{π} + 12 n - 3

Simplificar

\frac{6 arccos ( \frac{13}{30} )}{π} - 3 : \frac{6 arccos ( \frac{13}{30} ) - 3 π}{π}

\frac{6 arccos ( \frac{13}{30} )}{π} - 3

Convertir a fracción:

3 = \frac{3 π}{π}

= \frac{6 arccos ( \frac{13}{30} )}{π} - \frac{3 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 arccos ( \frac{13}{30} ) - 3 π}{π}

x < \frac{6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n

Combinar los rangos

x > \frac{- 6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n and x < \frac{6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n

Mezclar intervalos sobrepuestos

\frac{- 6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n < x < \frac{6 arccos ( \frac{13}{30} ) - 3 π}{π} + 12 n

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