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1=7cos(pi/3 t)

Solución

1 = 7 cos (\frac{π}{3} t)

Solución

t = \frac{3 \cdot 1.42744 \dots}{π} + 6 n, t = 6 - \frac{3 \cdot 1.42744 \dots}{π} + 6 n

Grados

t = 78.10063 \dots^{\circ} + 343.77467 \dots^{\circ} n, t = 265.67404 \dots^{\circ} + 343.77467 \dots^{\circ} n

Pasos de solución

1 = 7 cos (\frac{π}{3} t)

Intercambiar lados

7 cos (\frac{π}{3} t) = 1

Dividir ambos lados entre

7

7 cos (\frac{π}{3} t) = 1

Dividir ambos lados entre

7

\frac{7 cos ( \frac{π}{3} t )}{7} = \frac{1}{7}

Simplificar

cos (\frac{π}{3} t) = \frac{1}{7}

cos (\frac{π}{3} t) = \frac{1}{7}

Aplicar propiedades trigonométricas inversas

cos (\frac{π}{3} t) = \frac{1}{7}

Soluciones generales para

cos (\frac{π}{3} t) = \frac{1}{7}

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

\frac{π}{3} t = arccos (\frac{1}{7}) + 2 πn, \frac{π}{3} t = 2 π - arccos (\frac{1}{7}) + 2 πn

\frac{π}{3} t = arccos (\frac{1}{7}) + 2 πn, \frac{π}{3} t = 2 π - arccos (\frac{1}{7}) + 2 πn

Resolver

\frac{π}{3} t = arccos (\frac{1}{7}) + 2 πn : t = \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

\frac{π}{3} t = arccos (\frac{1}{7}) + 2 πn

Multiplicar ambos lados por

3

\frac{π}{3} t = arccos (\frac{1}{7}) + 2 πn

Multiplicar ambos lados por

3

3 \cdot \frac{π}{3} t = 3 arccos (\frac{1}{7}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{π}{3} t = 3 arccos (\frac{1}{7}) + 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{1}{7}) + 3 \cdot 2 πn : 3 arccos (\frac{1}{7}) + 6 πn

3 arccos (\frac{1}{7}) + 3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= 3 arccos (\frac{1}{7}) + 6 πn

π t = 3 arccos (\frac{1}{7}) + 6 πn

π t = 3 arccos (\frac{1}{7}) + 6 πn

π t = 3 arccos (\frac{1}{7}) + 6 πn

Dividir ambos lados entre

π

π t = 3 arccos (\frac{1}{7}) + 6 πn

Dividir ambos lados entre

π

\frac{π t}{π} = \frac{3 arccos ( \frac{1}{7} )}{π} + \frac{6 πn}{π}

Simplificar

t = \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

t = \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

Resolver

\frac{π}{3} t = 2 π - arccos (\frac{1}{7}) + 2 πn : t = 6 - \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

\frac{π}{3} t = 2 π - arccos (\frac{1}{7}) + 2 πn

Multiplicar ambos lados por

3

\frac{π}{3} t = 2 π - arccos (\frac{1}{7}) + 2 πn

Multiplicar ambos lados por

3

3 \cdot \frac{π}{3} t = 3 \cdot 2 π - 3 arccos (\frac{1}{7}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{π}{3} t = 3 \cdot 2 π - 3 arccos (\frac{1}{7}) + 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 \cdot 2 π - 3 arccos (\frac{1}{7}) + 3 \cdot 2 πn : 6 π - 3 arccos (\frac{1}{7}) + 6 πn

3 \cdot 2 π - 3 arccos (\frac{1}{7}) + 3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= 6 π - 3 arccos (\frac{1}{7}) + 6 πn

π t = 6 π - 3 arccos (\frac{1}{7}) + 6 πn

π t = 6 π - 3 arccos (\frac{1}{7}) + 6 πn

π t = 6 π - 3 arccos (\frac{1}{7}) + 6 πn

Dividir ambos lados entre

π

π t = 6 π - 3 arccos (\frac{1}{7}) + 6 πn

Dividir ambos lados entre

π

\frac{π t}{π} = \frac{6 π}{π} - \frac{3 arccos ( \frac{1}{7} )}{π} + \frac{6 πn}{π}

Simplificar

\frac{π t}{π} = \frac{6 π}{π} - \frac{3 arccos ( \frac{1}{7} )}{π} + \frac{6 πn}{π}

Simplificar

\frac{π t}{π} : t

\frac{π t}{π}

Eliminar los terminos comunes:

π

= t

Simplificar

\frac{6 π}{π} - \frac{3 arccos ( \frac{1}{7} )}{π} + \frac{6 πn}{π} : 6 - \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

\frac{6 π}{π} - \frac{3 arccos ( \frac{1}{7} )}{π} + \frac{6 πn}{π}

Cancelar

\frac{6 π}{π} : 6

\frac{6 π}{π}

Eliminar los terminos comunes:

π

= 6

= 6 - \frac{3 arccos ( \frac{1}{7} )}{π} + \frac{6 πn}{π}

Cancelar

\frac{6 πn}{π} : 6 n

\frac{6 πn}{π}

Eliminar los terminos comunes:

π

= 6 n

= 6 - \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

t = 6 - \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

t = 6 - \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

t = 6 - \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

t = \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n, t = 6 - \frac{3 arccos ( \frac{1}{7} )}{π} + 6 n

Mostrar soluciones en forma decimal

t = \frac{3 \cdot 1.42744 \dots}{π} + 6 n, t = 6 - \frac{3 \cdot 1.42744 \dots}{π} + 6 n

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