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1/3 =cos((pix)/(12))

Solución

\frac{1}{3} = cos (\frac{π x}{12})

Solución

x = \frac{12 \cdot 1.23095 \dots}{π} + 24 n, x = 24 - \frac{12 \cdot 1.23095 \dots}{π} + 24 n

Grados

x = 269.40009 \dots^{\circ} + 1375.09870 \dots^{\circ} n, x = 1105.69861 \dots^{\circ} + 1375.09870 \dots^{\circ} n

Pasos de solución

\frac{1}{3} = cos (\frac{π x}{12})

Intercambiar lados

cos (\frac{π x}{12}) = \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cos (\frac{π x}{12}) = \frac{1}{3}

Soluciones generales para

cos (\frac{π x}{12}) = \frac{1}{3}

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

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn, \frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn, \frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

Resolver

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn : x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn

Multiplicar ambos lados por

12

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn

Multiplicar ambos lados por

12

\frac{12 π x}{12} = 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

Simplificar

\frac{12 π x}{12} = 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

Simplificar

\frac{12 π x}{12} : π x

\frac{12 π x}{12}

Dividir:

\frac{12}{12} = 1

= π x

Simplificar

12 arccos (\frac{1}{3}) + 12 \cdot 2 πn : 12 arccos (\frac{1}{3}) + 24 πn

12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

Multiplicar los numeros:

12 \cdot 2 = 24

= 12 arccos (\frac{1}{3}) + 24 πn

π x = 12 arccos (\frac{1}{3}) + 24 πn

π x = 12 arccos (\frac{1}{3}) + 24 πn

π x = 12 arccos (\frac{1}{3}) + 24 πn

Dividir ambos lados entre

π

π x = 12 arccos (\frac{1}{3}) + 24 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

Simplificar

x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

Resolver

\frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn : x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

\frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

Multiplicar ambos lados por

12

\frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

Multiplicar ambos lados por

12

\frac{12 π x}{12} = 12 \cdot 2 π - 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

Simplificar

\frac{12 π x}{12} = 12 \cdot 2 π - 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

Simplificar

\frac{12 π x}{12} : π x

\frac{12 π x}{12}

Dividir:

\frac{12}{12} = 1

= π x

Simplificar

12 \cdot 2 π - 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn : 24 π - 12 arccos (\frac{1}{3}) + 24 πn

12 \cdot 2 π - 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

Multiplicar los numeros:

12 \cdot 2 = 24

= 24 π - 12 arccos (\frac{1}{3}) + 24 πn

π x = 24 π - 12 arccos (\frac{1}{3}) + 24 πn

π x = 24 π - 12 arccos (\frac{1}{3}) + 24 πn

π x = 24 π - 12 arccos (\frac{1}{3}) + 24 πn

Dividir ambos lados entre

π

π x = 24 π - 12 arccos (\frac{1}{3}) + 24 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{24 π}{π} - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

Simplificar

\frac{π x}{π} = \frac{24 π}{π} - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{24 π}{π} - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π} : 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

\frac{24 π}{π} - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

Cancelar

\frac{24 π}{π} : 24

\frac{24 π}{π}

Eliminar los terminos comunes:

π

= 24

= 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

Cancelar

\frac{24 πn}{π} : 24 n

\frac{24 πn}{π}

Eliminar los terminos comunes:

π

= 24 n

= 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n, x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

Mostrar soluciones en forma decimal

x = \frac{12 \cdot 1.23095 \dots}{π} + 24 n, x = 24 - \frac{12 \cdot 1.23095 \dots}{π} + 24 n

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