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11=12+3.1cos((2pi)/(365)t)

Solución

11 = 12 + 3.1 cos (\frac{2 π}{365} t)

Solución

t = \frac{365 \cdot 1.89925 \dots}{2 π} + 365 n, t = - \frac{365 \cdot 1.89925 \dots}{2 π} + 365 n

Grados

t = 6321.46852 \dots^{\circ} + 20912.95952 \dots^{\circ} n, t = - 6321.46852 \dots^{\circ} + 20912.95952 \dots^{\circ} n

Pasos de solución

11 = 12 + 3.1 cos (\frac{2 π}{365} t)

Intercambiar lados

12 + 3.1 cos (\frac{2 π}{365} t) = 11

Multiplicar ambos lados por

10

12 + 3.1 cos (\frac{2 π}{365} t) = 11

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

12 \cdot 10 + 3.1 cos (\frac{2 π}{365} t) \cdot 10 = 11 \cdot 10

Simplificar

120 + 31 cos (\frac{2 π}{365} t) = 110

120 + 31 cos (\frac{2 π}{365} t) = 110

Mover

120

al lado derecho

120 + 31 cos (\frac{2 π}{365} t) = 110

Restar

120

de ambos lados

120 + 31 cos (\frac{2 π}{365} t) - 120 = 110 - 120

Simplificar

31 cos (\frac{2 π}{365} t) = - 10

31 cos (\frac{2 π}{365} t) = - 10

Dividir ambos lados entre

31

31 cos (\frac{2 π}{365} t) = - 10

Dividir ambos lados entre

31

\frac{31 cos ( \frac{2 π}{365} t )}{31} = \frac{- 10}{31}

Simplificar

cos (\frac{2 π}{365} t) = - \frac{10}{31}

cos (\frac{2 π}{365} t) = - \frac{10}{31}

Aplicar propiedades trigonométricas inversas

cos (\frac{2 π}{365} t) = - \frac{10}{31}

Soluciones generales para

cos (\frac{2 π}{365} t) = - \frac{10}{31}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

\frac{2 π}{365} t = arccos (- \frac{10}{31}) + 2 πn, \frac{2 π}{365} t = - arccos (- \frac{10}{31}) + 2 πn

\frac{2 π}{365} t = arccos (- \frac{10}{31}) + 2 πn, \frac{2 π}{365} t = - arccos (- \frac{10}{31}) + 2 πn

Resolver

\frac{2 π}{365} t = arccos (- \frac{10}{31}) + 2 πn : t = \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

\frac{2 π}{365} t = arccos (- \frac{10}{31}) + 2 πn

Multiplicar ambos lados por

365

\frac{2 π}{365} t = arccos (- \frac{10}{31}) + 2 πn

Multiplicar ambos lados por

365

365 \cdot \frac{2 π}{365} t = 365 arccos (- \frac{10}{31}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} t = 365 arccos (- \frac{10}{31}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} t : 2 π t

365 \cdot \frac{2 π}{365} t

Multiplicar fracciones:

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

= \frac{2 \cdot 365 π}{365} t

Eliminar los terminos comunes:

365

= t \cdot 2 π

Simplificar

365 arccos (- \frac{10}{31}) + 365 \cdot 2 πn : 365 arccos (- \frac{10}{31}) + 730 πn

365 arccos (- \frac{10}{31}) + 365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= 365 arccos (- \frac{10}{31}) + 730 πn

2 π t = 365 arccos (- \frac{10}{31}) + 730 πn

2 π t = 365 arccos (- \frac{10}{31}) + 730 πn

2 π t = 365 arccos (- \frac{10}{31}) + 730 πn

Dividir ambos lados entre

2 π

2 π t = 365 arccos (- \frac{10}{31}) + 730 πn

Dividir ambos lados entre

2 π

\frac{2 π t}{2 π} = \frac{365 arccos ( - \frac{10}{31} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = \frac{365 arccos ( - \frac{10}{31} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π t}{π}

Eliminar los terminos comunes:

π

= t

Simplificar

\frac{365 arccos ( - \frac{10}{31} )}{2 π} + \frac{730 πn}{2 π} : \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

\frac{365 arccos ( - \frac{10}{31} )}{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{10}{31} )}{2 π} + 365 n

t = \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

t = \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

t = \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

Resolver

\frac{2 π}{365} t = - arccos (- \frac{10}{31}) + 2 πn : t = - \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

\frac{2 π}{365} t = - arccos (- \frac{10}{31}) + 2 πn

Multiplicar ambos lados por

365

\frac{2 π}{365} t = - arccos (- \frac{10}{31}) + 2 πn

Multiplicar ambos lados por

365

365 \cdot \frac{2 π}{365} t = - 365 arccos (- \frac{10}{31}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} t = - 365 arccos (- \frac{10}{31}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} t : 2 π t

365 \cdot \frac{2 π}{365} t

Multiplicar fracciones:

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

= \frac{2 \cdot 365 π}{365} t

Eliminar los terminos comunes:

365

= t \cdot 2 π

Simplificar

- 365 arccos (- \frac{10}{31}) + 365 \cdot 2 πn : - 365 arccos (- \frac{10}{31}) + 730 πn

- 365 arccos (- \frac{10}{31}) + 365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= - 365 arccos (- \frac{10}{31}) + 730 πn

2 π t = - 365 arccos (- \frac{10}{31}) + 730 πn

2 π t = - 365 arccos (- \frac{10}{31}) + 730 πn

2 π t = - 365 arccos (- \frac{10}{31}) + 730 πn

Dividir ambos lados entre

2 π

2 π t = - 365 arccos (- \frac{10}{31}) + 730 πn

Dividir ambos lados entre

2 π

\frac{2 π t}{2 π} = - \frac{365 arccos ( - \frac{10}{31} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = - \frac{365 arccos ( - \frac{10}{31} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π t}{π}

Eliminar los terminos comunes:

π

= t

Simplificar

- \frac{365 arccos ( - \frac{10}{31} )}{2 π} + \frac{730 πn}{2 π} : - \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

- \frac{365 arccos ( - \frac{10}{31} )}{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{10}{31} )}{2 π} + 365 n

t = - \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

t = - \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

t = - \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

t = \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n, t = - \frac{365 arccos ( - \frac{10}{31} )}{2 π} + 365 n

Mostrar soluciones en forma decimal

t = \frac{365 \cdot 1.89925 \dots}{2 π} + 365 n, t = - \frac{365 \cdot 1.89925 \dots}{2 π} + 365 n

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