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40+40cos((2pix)/9)=50

Solución

40 + 40 cos (\frac{2 π x}{9}) = 50

Solución

x = \frac{9 \cdot 1.31811 \dots}{2 π} + 9 n, x = 9 - \frac{9 \cdot 1.31811 \dots}{2 π} + 9 n

Grados

x = 108.17799 \dots^{\circ} + 515.66201 \dots^{\circ} n, x = 407.48402 \dots^{\circ} + 515.66201 \dots^{\circ} n

Pasos de solución

40 + 40 cos (\frac{2 π x}{9}) = 50

Mover

40

al lado derecho

40 + 40 cos (\frac{2 π x}{9}) = 50

Restar

40

de ambos lados

40 + 40 cos (\frac{2 π x}{9}) - 40 = 50 - 40

Simplificar

40 cos (\frac{2 π x}{9}) = 10

40 cos (\frac{2 π x}{9}) = 10

Dividir ambos lados entre

40

40 cos (\frac{2 π x}{9}) = 10

Dividir ambos lados entre

40

\frac{40 cos ( \frac{2 π x}{9} )}{40} = \frac{10}{40}

Simplificar

cos (\frac{2 π x}{9}) = \frac{1}{4}

cos (\frac{2 π x}{9}) = \frac{1}{4}

Aplicar propiedades trigonométricas inversas

cos (\frac{2 π x}{9}) = \frac{1}{4}

Soluciones generales para

cos (\frac{2 π x}{9}) = \frac{1}{4}

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

\frac{2 π x}{9} = arccos (\frac{1}{4}) + 2 πn, \frac{2 π x}{9} = 2 π - arccos (\frac{1}{4}) + 2 πn

\frac{2 π x}{9} = arccos (\frac{1}{4}) + 2 πn, \frac{2 π x}{9} = 2 π - arccos (\frac{1}{4}) + 2 πn

Resolver

\frac{2 π x}{9} = arccos (\frac{1}{4}) + 2 πn : x = \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

\frac{2 π x}{9} = arccos (\frac{1}{4}) + 2 πn

Multiplicar ambos lados por

9

\frac{2 π x}{9} = arccos (\frac{1}{4}) + 2 πn

Multiplicar ambos lados por

9

\frac{9 \cdot 2 π x}{9} = 9 arccos (\frac{1}{4}) + 9 \cdot 2 πn

Simplificar

\frac{9 \cdot 2 π x}{9} = 9 arccos (\frac{1}{4}) + 9 \cdot 2 πn

Simplificar

\frac{9 \cdot 2 π x}{9} : 2 π x

\frac{9 \cdot 2 π x}{9}

Multiplicar los numeros:

9 \cdot 2 = 18

= \frac{18 π x}{9}

Dividir:

\frac{18}{9} = 2

= 2 π x

Simplificar

9 arccos (\frac{1}{4}) + 9 \cdot 2 πn : 9 arccos (\frac{1}{4}) + 18 πn

9 arccos (\frac{1}{4}) + 9 \cdot 2 πn

Multiplicar los numeros:

9 \cdot 2 = 18

= 9 arccos (\frac{1}{4}) + 18 πn

2 π x = 9 arccos (\frac{1}{4}) + 18 πn

2 π x = 9 arccos (\frac{1}{4}) + 18 πn

2 π x = 9 arccos (\frac{1}{4}) + 18 πn

Dividir ambos lados entre

2 π

2 π x = 9 arccos (\frac{1}{4}) + 18 πn

Dividir ambos lados entre

2 π

\frac{2 π x}{2 π} = \frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π}

Simplificar

\frac{2 π x}{2 π} = \frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π}

Simplificar

\frac{2 π x}{2 π} : x

\frac{2 π x}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π} : \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

\frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π}

Cancelar

\frac{18 πn}{2 π} : 9 n

\frac{18 πn}{2 π}

Cancelar

\frac{18 πn}{2 π} : 9 n

\frac{18 πn}{2 π}

Dividir:

\frac{18}{2} = 9

= \frac{9 πn}{π}

Eliminar los terminos comunes:

π

= 9 n

= 9 n

= \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

x = \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

x = \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

x = \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

Resolver

\frac{2 π x}{9} = 2 π - arccos (\frac{1}{4}) + 2 πn : x = 9 - \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

\frac{2 π x}{9} = 2 π - arccos (\frac{1}{4}) + 2 πn

Multiplicar ambos lados por

9

\frac{2 π x}{9} = 2 π - arccos (\frac{1}{4}) + 2 πn

Multiplicar ambos lados por

9

\frac{9 \cdot 2 π x}{9} = 9 \cdot 2 π - 9 arccos (\frac{1}{4}) + 9 \cdot 2 πn

Simplificar

\frac{9 \cdot 2 π x}{9} = 9 \cdot 2 π - 9 arccos (\frac{1}{4}) + 9 \cdot 2 πn

Simplificar

\frac{9 \cdot 2 π x}{9} : 2 π x

\frac{9 \cdot 2 π x}{9}

Multiplicar los numeros:

9 \cdot 2 = 18

= \frac{18 π x}{9}

Dividir:

\frac{18}{9} = 2

= 2 π x

Simplificar

9 \cdot 2 π - 9 arccos (\frac{1}{4}) + 9 \cdot 2 πn : 18 π - 9 arccos (\frac{1}{4}) + 18 πn

9 \cdot 2 π - 9 arccos (\frac{1}{4}) + 9 \cdot 2 πn

Multiplicar los numeros:

9 \cdot 2 = 18

= 18 π - 9 arccos (\frac{1}{4}) + 18 πn

2 π x = 18 π - 9 arccos (\frac{1}{4}) + 18 πn

2 π x = 18 π - 9 arccos (\frac{1}{4}) + 18 πn

2 π x = 18 π - 9 arccos (\frac{1}{4}) + 18 πn

Dividir ambos lados entre

2 π

2 π x = 18 π - 9 arccos (\frac{1}{4}) + 18 πn

Dividir ambos lados entre

2 π

\frac{2 π x}{2 π} = \frac{18 π}{2 π} - \frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π}

Simplificar

\frac{2 π x}{2 π} = \frac{18 π}{2 π} - \frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π}

Simplificar

\frac{2 π x}{2 π} : x

\frac{2 π x}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{18 π}{2 π} - \frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π} : 9 - \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

\frac{18 π}{2 π} - \frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π}

Cancelar

\frac{18 π}{2 π} : 9

\frac{18 π}{2 π}

Cancelar

\frac{18 π}{2 π} : 9

\frac{18 π}{2 π}

Dividir:

\frac{18}{2} = 9

= \frac{9 π}{π}

Eliminar los terminos comunes:

π

= 9

= 9

= 9 - \frac{9 arccos ( \frac{1}{4} )}{2 π} + \frac{18 πn}{2 π}

Cancelar

\frac{18 πn}{2 π} : 9 n

\frac{18 πn}{2 π}

Cancelar

\frac{18 πn}{2 π} : 9 n

\frac{18 πn}{2 π}

Dividir:

\frac{18}{2} = 9

= \frac{9 πn}{π}

Eliminar los terminos comunes:

π

= 9 n

= 9 n

= 9 - \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

x = 9 - \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

x = 9 - \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

x = 9 - \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

x = \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n, x = 9 - \frac{9 arccos ( \frac{1}{4} )}{2 π} + 9 n

Mostrar soluciones en forma decimal

x = \frac{9 \cdot 1.31811 \dots}{2 π} + 9 n, x = 9 - \frac{9 \cdot 1.31811 \dots}{2 π} + 9 n

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