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0=12cos(pi/3 t)+8

Solución

0 = 12 cos (\frac{π}{3} t) + 8

Solución

t = \frac{3 \cdot 2.30052 \dots}{π} + 6 n, t = - \frac{3 \cdot 2.30052 \dots}{π} + 6 n

Grados

t = 125.86957 \dots^{\circ} + 343.77467 \dots^{\circ} n, t = - 125.86957 \dots^{\circ} + 343.77467 \dots^{\circ} n

Pasos de solución

0 = 12 cos (\frac{π}{3} t) + 8

Intercambiar lados

12 cos (\frac{π}{3} t) + 8 = 0

Mover

8

al lado derecho

12 cos (\frac{π}{3} t) + 8 = 0

Restar

8

de ambos lados

12 cos (\frac{π}{3} t) + 8 - 8 = 0 - 8

Simplificar

12 cos (\frac{π}{3} t) = - 8

12 cos (\frac{π}{3} t) = - 8

Dividir ambos lados entre

12

12 cos (\frac{π}{3} t) = - 8

Dividir ambos lados entre

12

\frac{12 cos ( \frac{π}{3} t )}{12} = \frac{- 8}{12}

Simplificar

\frac{12 cos ( \frac{π}{3} t )}{12} = \frac{- 8}{12}

Simplificar

\frac{12 cos ( \frac{π}{3} t )}{12} : cos (\frac{π}{3} t)

\frac{12 cos ( \frac{π}{3} t )}{12}

Dividir:

\frac{12}{12} = 1

= cos (\frac{π}{3} t)

Simplificar

\frac{- 8}{12} : - \frac{2}{3}

\frac{- 8}{12}

Aplicar las propiedades de las fracciones:

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

= - \frac{8}{12}

Eliminar los terminos comunes:

4

= - \frac{2}{3}

cos (\frac{π}{3} t) = - \frac{2}{3}

cos (\frac{π}{3} t) = - \frac{2}{3}

cos (\frac{π}{3} t) = - \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (\frac{π}{3} t) = - \frac{2}{3}

Soluciones generales para

cos (\frac{π}{3} t) = - \frac{2}{3}

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

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

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

Resolver

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

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

Multiplicar ambos lados por

3

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

Multiplicar ambos lados por

3

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

Simplificar

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

Simplificar

3 \cdot \frac{π}{3} t : π t

3 \cdot \frac{π}{3} t

Multiplicar fracciones:

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

= \frac{3 π}{3} t

Eliminar los terminos comunes:

3

= t π

Simplificar

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

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

Multiplicar los numeros:

3 \cdot 2 = 6

= 3 arccos (- \frac{2}{3}) + 6 πn

π t = 3 arccos (- \frac{2}{3}) + 6 πn

π t = 3 arccos (- \frac{2}{3}) + 6 πn

π t = 3 arccos (- \frac{2}{3}) + 6 πn

Dividir ambos lados entre

π

π t = 3 arccos (- \frac{2}{3}) + 6 πn

Dividir ambos lados entre

π

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

Simplificar

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

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

Resolver

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

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

Multiplicar ambos lados por

3

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

Multiplicar ambos lados por

3

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

Simplificar

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

Simplificar

3 \cdot \frac{π}{3} t : π t

3 \cdot \frac{π}{3} t

Multiplicar fracciones:

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

= \frac{3 π}{3} t

Eliminar los terminos comunes:

3

= t π

Simplificar

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

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

Multiplicar los numeros:

3 \cdot 2 = 6

= - 3 arccos (- \frac{2}{3}) + 6 πn

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

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

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

Dividir ambos lados entre

π

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

Dividir ambos lados entre

π

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

Simplificar

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

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

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

Mostrar soluciones en forma decimal

t = \frac{3 \cdot 2.30052 \dots}{π} + 6 n, t = - \frac{3 \cdot 2.30052 \dots}{π} + 6 n

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