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3.87sin((2pi(t+101.75))/(365))+11.7=14

Solución

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) + 11.7 = 14

Solución

t = \frac{365 \cdot 0.63641 \dots}{2 π} + 365 n - 101.75, t = \frac{365}{2} - \frac{365 \cdot 0.63641 \dots}{2 π} + 365 n - 101.75

Grados

t = - 3711.60484 \dots^{\circ} + 20912.95952 \dots^{\circ} n, t = 2508.39347 \dots^{\circ} + 20912.95952 \dots^{\circ} n

Pasos de solución

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) + 11.7 = 14

Multiplicar ambos lados por

100

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) + 11.7 = 14

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) \cdot 100 + 11.7 \cdot 100 = 14 \cdot 100

Simplificar

387 sin (\frac{2 π ( t + 101.75 )}{365}) + 1170 = 1400

387 sin (\frac{2 π ( t + 101.75 )}{365}) + 1170 = 1400

Mover

1170

al lado derecho

387 sin (\frac{2 π ( t + 101.75 )}{365}) + 1170 = 1400

Restar

1170

de ambos lados

387 sin (\frac{2 π ( t + 101.75 )}{365}) + 1170 - 1170 = 1400 - 1170

Simplificar

387 sin (\frac{2 π ( t + 101.75 )}{365}) = 230

387 sin (\frac{2 π ( t + 101.75 )}{365}) = 230

Dividir ambos lados entre

387

387 sin (\frac{2 π ( t + 101.75 )}{365}) = 230

Dividir ambos lados entre

387

\frac{387 sin ( \frac{2 π ( t + 101.75 )}{365} )}{387} = \frac{230}{387}

Simplificar

sin (\frac{2 π ( t + 101.75 )}{365}) = \frac{230}{387}

sin (\frac{2 π ( t + 101.75 )}{365}) = \frac{230}{387}

Aplicar propiedades trigonométricas inversas

sin (\frac{2 π ( t + 101.75 )}{365}) = \frac{230}{387}

Soluciones generales para

sin (\frac{2 π ( t + 101.75 )}{365}) = \frac{230}{387}

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

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn, \frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn, \frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

Resolver

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn : t = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn

Multiplicar ambos lados por

365

\frac{2 π ( t + 101.75 )}{365} = arcsin (\frac{230}{387}) + 2 πn

Multiplicar ambos lados por

365

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

Simplificar

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

Simplificar

\frac{365 \cdot 2 π ( t + 101.75 )}{365} : 2 π (t + 101.75)

\frac{365 \cdot 2 π ( t + 101.75 )}{365}

Multiplicar los numeros:

365 \cdot 2 = 730

= \frac{730 π ( t + 101.75 )}{365}

Dividir:

\frac{730}{365} = 2

= 2 π (t + 101.75)

Simplificar

365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn : 365 arcsin (\frac{230}{387}) + 730 πn

365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 arcsin (\frac{230}{387}) + 730 πn

Dividir ambos lados entre

2 π

2 π (t + 101.75) = 365 arcsin (\frac{230}{387}) + 730 πn

Dividir ambos lados entre

2 π

\frac{2 π ( t + 101.75 )}{2 π} = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( t + 101.75 )}{2 π} = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( t + 101.75 )}{2 π} : t + 101.75

\frac{2 π ( t + 101.75 )}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π ( t + 101.75 )}{π}

Eliminar los terminos comunes:

π

= t + 101.75

Simplificar

\frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π} : \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

\frac{365 arcsin ( \frac{230}{387} )}{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{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

Mover

101.75

al lado derecho

t + 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

Restar

101.75

de ambos lados

t + 101.75 - 101.75 = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

Simplificar

t = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

t = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

Resolver

\frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn : t = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

\frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

Multiplicar ambos lados por

365

\frac{2 π ( t + 101.75 )}{365} = π - arcsin (\frac{230}{387}) + 2 πn

Multiplicar ambos lados por

365

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 π - 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

Simplificar

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 π - 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

Simplificar

\frac{365 \cdot 2 π ( t + 101.75 )}{365} : 2 π (t + 101.75)

\frac{365 \cdot 2 π ( t + 101.75 )}{365}

Multiplicar los numeros:

365 \cdot 2 = 730

= \frac{730 π ( t + 101.75 )}{365}

Dividir:

\frac{730}{365} = 2

= 2 π (t + 101.75)

Simplificar

365 π - 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn : 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

365 π - 365 arcsin (\frac{230}{387}) + 365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

2 π (t + 101.75) = 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

Dividir ambos lados entre

2 π

2 π (t + 101.75) = 365 π - 365 arcsin (\frac{230}{387}) + 730 πn

Dividir ambos lados entre

2 π

\frac{2 π ( t + 101.75 )}{2 π} = \frac{365 π}{2 π} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( t + 101.75 )}{2 π} = \frac{365 π}{2 π} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π ( t + 101.75 )}{2 π} : t + 101.75

\frac{2 π ( t + 101.75 )}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π ( t + 101.75 )}{π}

Eliminar los terminos comunes:

π

= t + 101.75

Simplificar

\frac{365 π}{2 π} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + \frac{730 πn}{2 π} : \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

\frac{365 π}{2 π} - \frac{365 arcsin ( \frac{230}{387} )}{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{230}{387} )}{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{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

t + 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

Mover

101.75

al lado derecho

t + 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n

Restar

101.75

de ambos lados

t + 101.75 - 101.75 = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

Simplificar

t = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

t = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

t = \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75, t = \frac{365}{2} - \frac{365 arcsin ( \frac{230}{387} )}{2 π} + 365 n - 101.75

Mostrar soluciones en forma decimal

t = \frac{365 \cdot 0.63641 \dots}{2 π} + 365 n - 101.75, t = \frac{365}{2} - \frac{365 \cdot 0.63641 \dots}{2 π} + 365 n - 101.75

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