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Popular >

21=24+8cos((pit)/6)

Solución

21 = 24 + 8 cos (\frac{π t}{6})

Solución

t = \frac{6 \cdot 1.95519 \dots}{π} + 12 n, t = - \frac{6 \cdot 1.95519 \dots}{π} + 12 n

Grados

t = 213.95067 \dots^{\circ} + 687.54935 \dots^{\circ} n, t = - 213.95067 \dots^{\circ} + 687.54935 \dots^{\circ} n

Pasos de solución

21 = 24 + 8 cos (\frac{π t}{6})

Intercambiar lados

24 + 8 cos (\frac{π t}{6}) = 21

Mover

24

al lado derecho

24 + 8 cos (\frac{π t}{6}) = 21

Restar

24

de ambos lados

24 + 8 cos (\frac{π t}{6}) - 24 = 21 - 24

Simplificar

8 cos (\frac{π t}{6}) = - 3

8 cos (\frac{π t}{6}) = - 3

Dividir ambos lados entre

8

8 cos (\frac{π t}{6}) = - 3

Dividir ambos lados entre

8

\frac{8 cos ( \frac{π t}{6} )}{8} = \frac{- 3}{8}

Simplificar

cos (\frac{π t}{6}) = - \frac{3}{8}

cos (\frac{π t}{6}) = - \frac{3}{8}

Aplicar propiedades trigonométricas inversas

cos (\frac{π t}{6}) = - \frac{3}{8}

Soluciones generales para

cos (\frac{π t}{6}) = - \frac{3}{8}

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

\frac{π t}{6} = arccos (- \frac{3}{8}) + 2 πn, \frac{π t}{6} = - arccos (- \frac{3}{8}) + 2 πn

\frac{π t}{6} = arccos (- \frac{3}{8}) + 2 πn, \frac{π t}{6} = - arccos (- \frac{3}{8}) + 2 πn

Resolver

\frac{π t}{6} = arccos (- \frac{3}{8}) + 2 πn : t = \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

\frac{π t}{6} = arccos (- \frac{3}{8}) + 2 πn

Multiplicar ambos lados por

6

\frac{π t}{6} = arccos (- \frac{3}{8}) + 2 πn

Multiplicar ambos lados por

6

\frac{6 π t}{6} = 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Simplificar

\frac{6 π t}{6} = 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Simplificar

\frac{6 π t}{6} : π t

\frac{6 π t}{6}

Dividir:

\frac{6}{6} = 1

= π t

Simplificar

6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn : 6 arccos (- \frac{3}{8}) + 12 πn

6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= 6 arccos (- \frac{3}{8}) + 12 πn

π t = 6 arccos (- \frac{3}{8}) + 12 πn

π t = 6 arccos (- \frac{3}{8}) + 12 πn

π t = 6 arccos (- \frac{3}{8}) + 12 πn

Dividir ambos lados entre

π

π t = 6 arccos (- \frac{3}{8}) + 12 πn

Dividir ambos lados entre

π

\frac{π t}{π} = \frac{6 arccos ( - \frac{3}{8} )}{π} + \frac{12 πn}{π}

Simplificar

t = \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

t = \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

Resolver

\frac{π t}{6} = - arccos (- \frac{3}{8}) + 2 πn : t = - \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

\frac{π t}{6} = - arccos (- \frac{3}{8}) + 2 πn

Multiplicar ambos lados por

6

\frac{π t}{6} = - arccos (- \frac{3}{8}) + 2 πn

Multiplicar ambos lados por

6

\frac{6 π t}{6} = - 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Simplificar

\frac{6 π t}{6} = - 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Simplificar

\frac{6 π t}{6} : π t

\frac{6 π t}{6}

Dividir:

\frac{6}{6} = 1

= π t

Simplificar

- 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn : - 6 arccos (- \frac{3}{8}) + 12 πn

- 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= - 6 arccos (- \frac{3}{8}) + 12 πn

π t = - 6 arccos (- \frac{3}{8}) + 12 πn

π t = - 6 arccos (- \frac{3}{8}) + 12 πn

π t = - 6 arccos (- \frac{3}{8}) + 12 πn

Dividir ambos lados entre

π

π t = - 6 arccos (- \frac{3}{8}) + 12 πn

Dividir ambos lados entre

π

\frac{π t}{π} = - \frac{6 arccos ( - \frac{3}{8} )}{π} + \frac{12 πn}{π}

Simplificar

t = - \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

t = - \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

t = \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n, t = - \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

Mostrar soluciones en forma decimal

t = \frac{6 \cdot 1.95519 \dots}{π} + 12 n, t = - \frac{6 \cdot 1.95519 \dots}{π} + 12 n

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