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Popular >

16=-10cos((2pi)/(150)t)+10

Solución

16 = - 10 cos (\frac{2 π}{150} t) + 10

Solución

t = \frac{75 \cdot 2.21429 \dots}{π} + 150 n, t = - \frac{75 \cdot 2.21429 \dots}{π} + 150 n

Grados

t = 3028.79570 \dots^{\circ} + 8594.36692 \dots^{\circ} n, t = - 3028.79570 \dots^{\circ} + 8594.36692 \dots^{\circ} n

Pasos de solución

16 = - 10 cos (\frac{2 π}{150} t) + 10

Intercambiar lados

- 10 cos (\frac{2 π}{150} t) + 10 = 16

Mover

10

al lado derecho

- 10 cos (\frac{2 π}{150} t) + 10 = 16

Restar

10

de ambos lados

- 10 cos (\frac{2 π}{150} t) + 10 - 10 = 16 - 10

Simplificar

- 10 cos (\frac{2 π}{150} t) = 6

- 10 cos (\frac{2 π}{150} t) = 6

Dividir ambos lados entre

- 10

- 10 cos (\frac{2 π}{150} t) = 6

Dividir ambos lados entre

- 10

\frac{- 10 cos ( \frac{2 π}{150} t )}{- 10} = \frac{6}{- 10}

Simplificar

\frac{- 10 cos ( \frac{2 π}{150} t )}{- 10} = \frac{6}{- 10}

Simplificar

\frac{- 10 cos ( \frac{2 π}{150} t )}{- 10} : cos (\frac{2 π}{150} t)

\frac{- 10 cos ( \frac{2 π}{150} t )}{- 10}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{10 cos ( \frac{2 π}{150} t )}{10}

Dividir:

\frac{10}{10} = 1

= cos (\frac{2 π}{150} t)

Simplificar

\frac{6}{- 10} : - \frac{3}{5}

\frac{6}{- 10}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{6}{10}

Eliminar los terminos comunes:

2

= - \frac{3}{5}

cos (\frac{2 π}{150} t) = - \frac{3}{5}

cos (\frac{2 π}{150} t) = - \frac{3}{5}

cos (\frac{2 π}{150} t) = - \frac{3}{5}

Aplicar propiedades trigonométricas inversas

cos (\frac{2 π}{150} t) = - \frac{3}{5}

Soluciones generales para

cos (\frac{2 π}{150} t) = - \frac{3}{5}

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

\frac{2 π}{150} t = arccos (- \frac{3}{5}) + 2 πn, \frac{2 π}{150} t = - arccos (- \frac{3}{5}) + 2 πn

\frac{2 π}{150} t = arccos (- \frac{3}{5}) + 2 πn, \frac{2 π}{150} t = - arccos (- \frac{3}{5}) + 2 πn

Resolver

\frac{2 π}{150} t = arccos (- \frac{3}{5}) + 2 πn : t = \frac{75 arccos ( - \frac{3}{5} )}{π} + 150 n

\frac{2 π}{150} t = arccos (- \frac{3}{5}) + 2 πn

Multiplicar ambos lados por

75

\frac{2 π}{150} t = arccos (- \frac{3}{5}) + 2 πn

Multiplicar ambos lados por

75

75 \cdot \frac{2 π}{150} t = 75 arccos (- \frac{3}{5}) + 75 \cdot 2 πn

Simplificar

75 \cdot \frac{2 π}{150} t = 75 arccos (- \frac{3}{5}) + 75 \cdot 2 πn

Simplificar

75 \cdot \frac{2 π}{150} t : π t

75 \cdot \frac{2 π}{150} t

Multiplicar fracciones:

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

= \frac{2 π 75 t}{150}

Multiplicar los numeros:

2 \cdot 75 = 150

= \frac{150 π t}{150}

Dividir:

\frac{150}{150} = 1

= π t

Simplificar

75 arccos (- \frac{3}{5}) + 75 \cdot 2 πn : 75 arccos (- \frac{3}{5}) + 150 πn

75 arccos (- \frac{3}{5}) + 75 \cdot 2 πn

Multiplicar los numeros:

75 \cdot 2 = 150

= 75 arccos (- \frac{3}{5}) + 150 πn

π t = 75 arccos (- \frac{3}{5}) + 150 πn

π t = 75 arccos (- \frac{3}{5}) + 150 πn

π t = 75 arccos (- \frac{3}{5}) + 150 πn

Dividir ambos lados entre

π

π t = 75 arccos (- \frac{3}{5}) + 150 πn

Dividir ambos lados entre

π

\frac{π t}{π} = \frac{75 arccos ( - \frac{3}{5} )}{π} + \frac{150 πn}{π}

Simplificar

t = \frac{75 arccos ( - \frac{3}{5} )}{π} + 150 n

t = \frac{75 arccos ( - \frac{3}{5} )}{π} + 150 n

Resolver

\frac{2 π}{150} t = - arccos (- \frac{3}{5}) + 2 πn : t = - \frac{75 arccos ( - \frac{3}{5} )}{π} + 150 n

\frac{2 π}{150} t = - arccos (- \frac{3}{5}) + 2 πn

Multiplicar ambos lados por

75

\frac{2 π}{150} t = - arccos (- \frac{3}{5}) + 2 πn

Multiplicar ambos lados por

75

75 \cdot \frac{2 π}{150} t = - 75 arccos (- \frac{3}{5}) + 75 \cdot 2 πn

Simplificar

75 \cdot \frac{2 π}{150} t = - 75 arccos (- \frac{3}{5}) + 75 \cdot 2 πn

Simplificar

75 \cdot \frac{2 π}{150} t : π t

75 \cdot \frac{2 π}{150} t

Multiplicar fracciones:

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

= \frac{2 π 75 t}{150}

Multiplicar los numeros:

2 \cdot 75 = 150

= \frac{150 π t}{150}

Dividir:

\frac{150}{150} = 1

= π t

Simplificar

- 75 arccos (- \frac{3}{5}) + 75 \cdot 2 πn : - 75 arccos (- \frac{3}{5}) + 150 πn

- 75 arccos (- \frac{3}{5}) + 75 \cdot 2 πn

Multiplicar los numeros:

75 \cdot 2 = 150

= - 75 arccos (- \frac{3}{5}) + 150 πn

π t = - 75 arccos (- \frac{3}{5}) + 150 πn

π t = - 75 arccos (- \frac{3}{5}) + 150 πn

π t = - 75 arccos (- \frac{3}{5}) + 150 πn

Dividir ambos lados entre

π

π t = - 75 arccos (- \frac{3}{5}) + 150 πn

Dividir ambos lados entre

π

\frac{π t}{π} = - \frac{75 arccos ( - \frac{3}{5} )}{π} + \frac{150 πn}{π}

Simplificar

t = - \frac{75 arccos ( - \frac{3}{5} )}{π} + 150 n

t = - \frac{75 arccos ( - \frac{3}{5} )}{π} + 150 n

t = \frac{75 arccos ( - \frac{3}{5} )}{π} + 150 n, t = - \frac{75 arccos ( - \frac{3}{5} )}{π} + 150 n

Mostrar soluciones en forma decimal

t = \frac{75 \cdot 2.21429 \dots}{π} + 150 n, t = - \frac{75 \cdot 2.21429 \dots}{π} + 150 n

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