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21cos((2pi)/(687)t)+228=220

Solución

21 cos (\frac{2 π}{687} t) + 228 = 220

Solución

t = \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n, t = - \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n

Grados

t = 12288.95420 \dots^{\circ} + 39362.20052 \dots^{\circ} n, t = - 12288.95420 \dots^{\circ} + 39362.20052 \dots^{\circ} n

Pasos de solución

21 cos (\frac{2 π}{687} t) + 228 = 220

Mover

228

al lado derecho

21 cos (\frac{2 π}{687} t) + 228 = 220

Restar

228

de ambos lados

21 cos (\frac{2 π}{687} t) + 228 - 228 = 220 - 228

Simplificar

21 cos (\frac{2 π}{687} t) = - 8

21 cos (\frac{2 π}{687} t) = - 8

Dividir ambos lados entre

21

21 cos (\frac{2 π}{687} t) = - 8

Dividir ambos lados entre

21

\frac{21 cos ( \frac{2 π}{687} t )}{21} = \frac{- 8}{21}

Simplificar

cos (\frac{2 π}{687} t) = - \frac{8}{21}

cos (\frac{2 π}{687} t) = - \frac{8}{21}

Aplicar propiedades trigonométricas inversas

cos (\frac{2 π}{687} t) = - \frac{8}{21}

Soluciones generales para

cos (\frac{2 π}{687} t) = - \frac{8}{21}

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

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn, \frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn, \frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

Resolver

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn : t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn

Multiplicar ambos lados por

687

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn

Multiplicar ambos lados por

687

687 \cdot \frac{2 π}{687} t = 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Simplificar

687 \cdot \frac{2 π}{687} t = 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Simplificar

687 \cdot \frac{2 π}{687} t : 2 π t

687 \cdot \frac{2 π}{687} t

Multiplicar fracciones:

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

= \frac{2 \cdot 687 π}{687} t

Eliminar los terminos comunes:

687

= t \cdot 2 π

Simplificar

687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn : 687 arccos (- \frac{8}{21}) + 1374 πn

687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Multiplicar los numeros:

687 \cdot 2 = 1374

= 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

Dividir ambos lados entre

2 π

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

Dividir ambos lados entre

2 π

\frac{2 π t}{2 π} = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 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{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π} : \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Cancelar

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

Cancelar

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

Dividir:

\frac{1374}{2} = 687

= \frac{687 πn}{π}

Eliminar los terminos comunes:

π

= 687 n

= 687 n

= \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

Resolver

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn : t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

Multiplicar ambos lados por

687

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

Multiplicar ambos lados por

687

687 \cdot \frac{2 π}{687} t = - 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Simplificar

687 \cdot \frac{2 π}{687} t = - 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Simplificar

687 \cdot \frac{2 π}{687} t : 2 π t

687 \cdot \frac{2 π}{687} t

Multiplicar fracciones:

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

= \frac{2 \cdot 687 π}{687} t

Eliminar los terminos comunes:

687

= t \cdot 2 π

Simplificar

- 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn : - 687 arccos (- \frac{8}{21}) + 1374 πn

- 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Multiplicar los numeros:

687 \cdot 2 = 1374

= - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

Dividir ambos lados entre

2 π

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

Dividir ambos lados entre

2 π

\frac{2 π t}{2 π} = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 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{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π} : - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

- \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Cancelar

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

Cancelar

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

Dividir:

\frac{1374}{2} = 687

= \frac{687 πn}{π}

Eliminar los terminos comunes:

π

= 687 n

= 687 n

= - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n, t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

Mostrar soluciones en forma decimal

t = \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n, t = - \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n

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