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32=37.3sin((2pi)/(365)(x-114))+26

Solución

32 = 37.3 sin (\frac{2 π}{365} (x - 114)) + 26

Solución

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}

Grados

x = 7069.45471 \dots^{\circ} + 20912.95952 \dots^{\circ} n, x = 16450.46277 \dots^{\circ} + 20912.95952 \dots^{\circ} n

Pasos de solución

32 = 37.3 sin (\frac{2 π}{365} (x - 114)) + 26

Intercambiar lados

37.3 sin (\frac{2 π}{365} (x - 114)) + 26 = 32

Multiplicar ambos lados por

10

37.3 sin (\frac{2 π}{365} (x - 114)) + 26 = 32

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

37.3 sin (\frac{2 π}{365} (x - 114)) \cdot 10 + 26 \cdot 10 = 32 \cdot 10

Simplificar

373 sin (\frac{2 π}{365} (x - 114)) + 260 = 320

373 sin (\frac{2 π}{365} (x - 114)) + 260 = 320

Mover

260

al lado derecho

373 sin (\frac{2 π}{365} (x - 114)) + 260 = 320

Restar

260

de ambos lados

373 sin (\frac{2 π}{365} (x - 114)) + 260 - 260 = 320 - 260

Simplificar

373 sin (\frac{2 π}{365} (x - 114)) = 60

373 sin (\frac{2 π}{365} (x - 114)) = 60

Dividir ambos lados entre

373

373 sin (\frac{2 π}{365} (x - 114)) = 60

Dividir ambos lados entre

373

\frac{373 sin ( \frac{2 π}{365} ( x - 114 ) )}{373} = \frac{60}{373}

Simplificar

sin (\frac{2 π}{365} (x - 114)) = \frac{60}{373}

sin (\frac{2 π}{365} (x - 114)) = \frac{60}{373}

Aplicar propiedades trigonométricas inversas

sin (\frac{2 π}{365} (x - 114)) = \frac{60}{373}

Soluciones generales para

sin (\frac{2 π}{365} (x - 114)) = \frac{60}{373}

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

\frac{2 π}{365} (x - 114) = arcsin (\frac{60}{373}) + 2 πn, \frac{2 π}{365} (x - 114) = π - arcsin (\frac{60}{373}) + 2 πn

\frac{2 π}{365} (x - 114) = arcsin (\frac{60}{373}) + 2 πn, \frac{2 π}{365} (x - 114) = π - arcsin (\frac{60}{373}) + 2 πn

Resolver

\frac{2 π}{365} (x - 114) = arcsin (\frac{60}{373}) + 2 πn : x = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114

\frac{2 π}{365} (x - 114) = arcsin (\frac{60}{373}) + 2 πn

Multiplicar ambos lados por

365

\frac{2 π}{365} (x - 114) = arcsin (\frac{60}{373}) + 2 πn

Multiplicar ambos lados por

365

365 \cdot \frac{2 π}{365} (x - 114) = 365 arcsin (\frac{60}{373}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} (x - 114) = 365 arcsin (\frac{60}{373}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} (x - 114) : 2 π (x - 114)

365 \cdot \frac{2 π}{365} (x - 114)

Multiplicar fracciones:

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

= \frac{2 \cdot 365 π}{365} (x - 114)

Eliminar los terminos comunes:

365

= (x - 114) \cdot 2 π

Simplificar

365 arcsin (\frac{60}{373}) + 365 \cdot 2 πn : 365 arcsin (\frac{60}{373}) + 730 πn

365 arcsin (\frac{60}{373}) + 365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= 365 arcsin (\frac{60}{373}) + 730 πn

2 π (x - 114) = 365 arcsin (\frac{60}{373}) + 730 πn

2 π (x - 114) = 365 arcsin (\frac{60}{373}) + 730 πn

2 π (x - 114) = 365 arcsin (\frac{60}{373}) + 730 πn

Dividir ambos lados entre

2 π

2 π (x - 114) = 365 arcsin (\frac{60}{373}) + 730 πn

Dividir ambos lados entre

2 π

\frac{2 π ( x - 114 )}{2 π} = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x - 114 )}{2 π} = \frac{365 arcsin ( \frac{60}{373} )}{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 los terminos comunes:

π

= x - 114

Simplificar

\frac{365 arcsin ( \frac{60}{373} )}{2 π} + \frac{730 πn}{2 π} : \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

\frac{365 arcsin ( \frac{60}{373} )}{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 arcsin ( \frac{60}{373} )}{2 π} + 365 n

x - 114 = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

x - 114 = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

x - 114 = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

Mover

114

al lado derecho

x - 114 = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

Sumar

114

a ambos lados

x - 114 + 114 = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114

Simplificar

x = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114

x = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114

Resolver

\frac{2 π}{365} (x - 114) = π - arcsin (\frac{60}{373}) + 2 πn : x = 365 n + \frac{593}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π}

\frac{2 π}{365} (x - 114) = π - arcsin (\frac{60}{373}) + 2 πn

Multiplicar ambos lados por

365

\frac{2 π}{365} (x - 114) = π - arcsin (\frac{60}{373}) + 2 πn

Multiplicar ambos lados por

365

365 \cdot \frac{2 π}{365} (x - 114) = 365 π - 365 arcsin (\frac{60}{373}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} (x - 114) = 365 π - 365 arcsin (\frac{60}{373}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} (x - 114) : 2 π (x - 114)

365 \cdot \frac{2 π}{365} (x - 114)

Multiplicar fracciones:

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

= \frac{2 \cdot 365 π}{365} (x - 114)

Eliminar los terminos comunes:

365

= (x - 114) \cdot 2 π

Simplificar

365 π - 365 arcsin (\frac{60}{373}) + 365 \cdot 2 πn : 365 π - 365 arcsin (\frac{60}{373}) + 730 πn

365 π - 365 arcsin (\frac{60}{373}) + 365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= 365 π - 365 arcsin (\frac{60}{373}) + 730 πn

2 π (x - 114) = 365 π - 365 arcsin (\frac{60}{373}) + 730 πn

2 π (x - 114) = 365 π - 365 arcsin (\frac{60}{373}) + 730 πn

2 π (x - 114) = 365 π - 365 arcsin (\frac{60}{373}) + 730 πn

Dividir ambos lados entre

2 π

2 π (x - 114) = 365 π - 365 arcsin (\frac{60}{373}) + 730 πn

Dividir ambos lados entre

2 π

\frac{2 π ( x - 114 )}{2 π} = \frac{365 π}{2 π} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( x - 114 )}{2 π} = \frac{365 π}{2 π} - \frac{365 arcsin ( \frac{60}{373} )}{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 los terminos comunes:

π

= x - 114

Simplificar

\frac{365 π}{2 π} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + \frac{730 πn}{2 π} : \frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

\frac{365 π}{2 π} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + \frac{730 πn}{2 π}

Cancelar

\frac{365 π}{2 π} : \frac{365}{2}

\frac{365 π}{2 π}

Eliminar los terminos comunes:

π

= \frac{365}{2}

= \frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{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}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

x - 114 = \frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

x - 114 = \frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

x - 114 = \frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

Mover

114

al lado derecho

x - 114 = \frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n

Sumar

114

a ambos lados

x - 114 + 114 = \frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114

Simplificar

x - 114 + 114 = \frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114

Simplificar

x - 114 + 114 : x

x - 114 + 114

Sumar elementos similares:

- 114 + 114 = 0

= x

Simplificar

\frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114 : 365 n + \frac{593}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π}

\frac{365}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114

Combinar las fracciones usando el mínimo común denominador:

\frac{593}{2}

114 + \frac{365}{2}

Convertir a fracción:

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

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

Ya que los denominadores son iguales, combinar las fracciones:

\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 los numeros:

114 \cdot 2 = 228

= 228 + 365

Sumar:

228 + 365 = 593

= 593

= \frac{593}{2}

= 365 n + \frac{593}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π}

x = 365 n + \frac{593}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π}

x = 365 n + \frac{593}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π}

x = 365 n + \frac{593}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π}

x = \frac{365 arcsin ( \frac{60}{373} )}{2 π} + 365 n + 114, x = 365 n + \frac{593}{2} - \frac{365 arcsin ( \frac{60}{373} )}{2 π}

Mostrar soluciones en 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}

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