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Popular Trigonometría >

13>2.5cos(((2pi)/(365))(x+9))+12

Solución

13 > 2.5 cos ((\frac{2 π}{365}) (x + 9)) + 12

Solución

\frac{365 arccos ( \frac{2}{5} ) - 18 π}{2 π} + 365 n < x < \frac{712 π - 365 arccos ( \frac{2}{5} )}{2 π} + 365 n

Notación de intervalos

(\frac{365 arccos ( \frac{2}{5} ) - 18 π}{2 π} + 365 n, \frac{712 π - 365 arccos ( \frac{2}{5} )}{2 π} + 365 n)

Decimal

58.34434 \dots + 365 n < x < 288.65565 \dots + 365 n

Pasos de solución

13 > 2.5 cos (\frac{2 π}{365} (x + 9)) + 12

Intercambiar lados

2.5 cos (\frac{2 π}{365} (x + 9)) + 12 < 13

Multiplicar ambos lados por

10

2.5 cos (\frac{2 π}{365} (x + 9)) + 12 < 13

Para eliminar los puntos decimales, multiplique por 10 por cada digito después del punto decimalHay un digito a la derecha del punto decimal, por lo que debe multiplicar por

10

2.5 cos (\frac{2 π}{365} (x + 9)) \cdot 10 + 12 \cdot 10 < 13 \cdot 10

Simplificar

25 cos (\frac{2 π}{365} (x + 9)) + 120 < 130

25 cos (\frac{2 π}{365} (x + 9)) + 120 < 130

Desplace

120

a la derecha

25 cos (\frac{2 π}{365} (x + 9)) + 120 < 130

Restar

120

de ambos lados

25 cos (\frac{2 π}{365} (x + 9)) + 120 - 120 < 130 - 120

Simplificar

25 cos (\frac{2 π}{365} (x + 9)) < 10

25 cos (\frac{2 π}{365} (x + 9)) < 10

Dividir ambos lados entre

25

25 cos (\frac{2 π}{365} (x + 9)) < 10

Dividir ambos lados entre

25

\frac{25 cos ( \frac{2 π}{365} ( x + 9 ) )}{25} < \frac{10}{25}

Simplificar

cos (\frac{2 π}{365} (x + 9)) < \frac{2}{5}

cos (\frac{2 π}{365} (x + 9)) < \frac{2}{5}

Para

cos (x) < a

, si

- 1 < a \leq 1

entonces

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

arccos (\frac{2}{5}) + 2 πn < \frac{2 π}{365} (x + 9) < 2 π - arccos (\frac{2}{5}) + 2 πn

a < u < b

entonces

a < u and u < b

arccos (\frac{2}{5}) + 2 πn < \frac{2 π}{365} (x + 9) and \frac{2 π}{365} (x + 9) < 2 π - arccos (\frac{2}{5}) + 2 πn

arccos (\frac{2}{5}) + 2 πn < \frac{2 π}{365} (x + 9) : x > \frac{365 arccos ( \frac{2}{5} ) - 18 π}{2 π} + 365 n

arccos (\frac{2}{5}) + 2 πn < \frac{2 π}{365} (x + 9)

Intercambiar lados

\frac{2 π}{365} (x + 9) > arccos (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

365

\frac{2 π}{365} (x + 9) > arccos (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

365

365 \cdot \frac{2 π}{365} (x + 9) > 365 arccos (\frac{2}{5}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} (x + 9) > 365 arccos (\frac{2}{5}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} (x + 9) : 2 π (x + 9)

365 \cdot \frac{2 π}{365} (x + 9)

Multiplicar fracciones:

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

= \frac{2 \cdot 365 π}{365} (x + 9)

Eliminar los terminos comunes:

365

= (x + 9) \cdot 2 π

Simplificar

365 arccos (\frac{2}{5}) + 365 \cdot 2 πn : 365 arccos (\frac{2}{5}) + 730 πn

365 arccos (\frac{2}{5}) + 365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= 365 arccos (\frac{2}{5}) + 730 πn

2 π (x + 9) > 365 arccos (\frac{2}{5}) + 730 πn

2 π (x + 9) > 365 arccos (\frac{2}{5}) + 730 πn

2 π (x + 9) > 365 arccos (\frac{2}{5}) + 730 πn

Dividir ambos lados entre

2 π

2 π (x + 9) > 365 arccos (\frac{2}{5}) + 730 πn

Dividir ambos lados entre

2 π

\frac{2 π ( x + 9 )}{2 π} > \frac{365 arccos ( \frac{2}{5} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x + 9 )}{2 π} > \frac{365 arccos ( \frac{2}{5} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x + 9 )}{2 π} : x + 9

\frac{2 π ( x + 9 )}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π ( x + 9 )}{π}

Eliminar los terminos comunes:

π

= x + 9

Simplificar

\frac{365 arccos ( \frac{2}{5} )}{2 π} + \frac{730 πn}{2 π} : \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

\frac{365 arccos ( \frac{2}{5} )}{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 los terminos comunes:

π

= 365 n

= 365 n

= \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

x + 9 > \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

x + 9 > \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

x + 9 > \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

Desplace

9

a la derecha

x + 9 > \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

Restar

9

de ambos lados

x + 9 - 9 > \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n - 9

Simplificar

x > \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n - 9

x > \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n - 9

Simplificar

\frac{365 arccos ( \frac{2}{5} )}{2 π} - 9 : \frac{365 arccos ( \frac{2}{5} ) - 18 π}{2 π}

\frac{365 arccos ( \frac{2}{5} )}{2 π} - 9

Convertir a fracción:

9 = \frac{9 \cdot 2 π}{2 π}

= \frac{365 arccos ( \frac{2}{5} )}{2 π} - \frac{9 \cdot 2 π}{2 π}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{365 arccos ( \frac{2}{5} ) - 9 \cdot 2 π}{2 π}

Multiplicar los numeros:

9 \cdot 2 = 18

= \frac{365 arccos ( \frac{2}{5} ) - 18 π}{2 π}

x > \frac{365 arccos ( \frac{2}{5} ) - 18 π}{2 π} + 365 n

\frac{2 π}{365} (x + 9) < 2 π - arccos (\frac{2}{5}) + 2 πn : x < \frac{712 π - 365 arccos ( \frac{2}{5} )}{2 π} + 365 n

\frac{2 π}{365} (x + 9) < 2 π - arccos (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

365

\frac{2 π}{365} (x + 9) < 2 π - arccos (\frac{2}{5}) + 2 πn

Multiplicar ambos lados por

365

365 \cdot \frac{2 π}{365} (x + 9) < 365 \cdot 2 π - 365 arccos (\frac{2}{5}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} (x + 9) < 365 \cdot 2 π - 365 arccos (\frac{2}{5}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} (x + 9) : 2 π (x + 9)

365 \cdot \frac{2 π}{365} (x + 9)

Multiplicar fracciones:

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

= \frac{2 \cdot 365 π}{365} (x + 9)

Eliminar los terminos comunes:

365

= (x + 9) \cdot 2 π

Simplificar

365 \cdot 2 π - 365 arccos (\frac{2}{5}) + 365 \cdot 2 πn : 730 π - 365 arccos (\frac{2}{5}) + 730 πn

365 \cdot 2 π - 365 arccos (\frac{2}{5}) + 365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= 730 π - 365 arccos (\frac{2}{5}) + 730 πn

2 π (x + 9) < 730 π - 365 arccos (\frac{2}{5}) + 730 πn

2 π (x + 9) < 730 π - 365 arccos (\frac{2}{5}) + 730 πn

2 π (x + 9) < 730 π - 365 arccos (\frac{2}{5}) + 730 πn

Dividir ambos lados entre

2 π

2 π (x + 9) < 730 π - 365 arccos (\frac{2}{5}) + 730 πn

Dividir ambos lados entre

2 π

\frac{2 π ( x + 9 )}{2 π} < \frac{730 π}{2 π} - \frac{365 arccos ( \frac{2}{5} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x + 9 )}{2 π} < \frac{730 π}{2 π} - \frac{365 arccos ( \frac{2}{5} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x + 9 )}{2 π} : x + 9

\frac{2 π ( x + 9 )}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π ( x + 9 )}{π}

Eliminar los terminos comunes:

π

= x + 9

Simplificar

\frac{730 π}{2 π} - \frac{365 arccos ( \frac{2}{5} )}{2 π} + \frac{730 πn}{2 π} : 365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

\frac{730 π}{2 π} - \frac{365 arccos ( \frac{2}{5} )}{2 π} + \frac{730 πn}{2 π}

Cancelar

\frac{730 π}{2 π} : 365

\frac{730 π}{2 π}

Cancelar

\frac{730 π}{2 π} : 365

\frac{730 π}{2 π}

Dividir:

\frac{730}{2} = 365

= \frac{365 π}{π}

Eliminar los terminos comunes:

π

= 365

= 365

= 365 - \frac{365 arccos ( \frac{2}{5} )}{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 los terminos comunes:

π

= 365 n

= 365 n

= 365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

x + 9 < 365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

x + 9 < 365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

x + 9 < 365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

Desplace

9

a la derecha

x + 9 < 365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n

Restar

9

de ambos lados

x + 9 - 9 < 365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n - 9

Simplificar

x + 9 - 9 < 365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n - 9

Simplificar

x + 9 - 9 : x

x + 9 - 9

Sumar elementos similares:

9 - 9 < 0

= x

Simplificar

365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n - 9 : 365 n + 356 - \frac{365 arccos ( \frac{2}{5} )}{2 π}

365 - \frac{365 arccos ( \frac{2}{5} )}{2 π} + 365 n - 9

Restar:

365 - 9 = 356

= 365 n + 356 - \frac{365 arccos ( \frac{2}{5} )}{2 π}

x < 365 n + 356 - \frac{365 arccos ( \frac{2}{5} )}{2 π}

x < 365 n + 356 - \frac{365 arccos ( \frac{2}{5} )}{2 π}

x < 365 n + 356 - \frac{365 arccos ( \frac{2}{5} )}{2 π}

Simplificar

356 - \frac{365 arccos ( \frac{2}{5} )}{2 π} : \frac{712 π - 365 arccos ( \frac{2}{5} )}{2 π}

356 - \frac{365 arccos ( \frac{2}{5} )}{2 π}

Convertir a fracción:

356 = \frac{356 \cdot 2 π}{2 π}

= \frac{356 \cdot 2 π}{2 π} - \frac{365 arccos ( \frac{2}{5} )}{2 π}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{356 \cdot 2 π - 365 arccos ( \frac{2}{5} )}{2 π}

Multiplicar los numeros:

356 \cdot 2 = 712

= \frac{712 π - 365 arccos ( \frac{2}{5} )}{2 π}

x < \frac{712 π - 365 arccos ( \frac{2}{5} )}{2 π} + 365 n

Combinar los rangos

x > \frac{365 arccos ( \frac{2}{5} ) - 18 π}{2 π} + 365 n and x < \frac{712 π - 365 arccos ( \frac{2}{5} )}{2 π} + 365 n

Mezclar intervalos sobrepuestos

\frac{365 arccos ( \frac{2}{5} ) - 18 π}{2 π} + 365 n < x < \frac{712 π - 365 arccos ( \frac{2}{5} )}{2 π} + 365 n

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