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Popular Trigonometría >

40cos((2pi)/3 t)-71=-80

Solución

40 cos (\frac{2 π}{3} t) - 71 = - 80

Solución

t = \frac{3 \cdot 1.79773 \dots}{2 π} + 3 n, t = - \frac{3 \cdot 1.79773 \dots}{2 π} + 3 n

Grados

t = 49.18025 \dots^{\circ} + 171.88733 \dots^{\circ} n, t = - 49.18025 \dots^{\circ} + 171.88733 \dots^{\circ} n

Pasos de solución

40 cos (\frac{2 π}{3} t) - 71 = - 80

Desplace

71

a la derecha

40 cos (\frac{2 π}{3} t) - 71 = - 80

Sumar

71

a ambos lados

40 cos (\frac{2 π}{3} t) - 71 + 71 = - 80 + 71

Simplificar

40 cos (\frac{2 π}{3} t) = - 9

40 cos (\frac{2 π}{3} t) = - 9

Dividir ambos lados entre

40

40 cos (\frac{2 π}{3} t) = - 9

Dividir ambos lados entre

40

\frac{40 cos ( \frac{2 π}{3} t )}{40} = \frac{- 9}{40}

Simplificar

cos (\frac{2 π}{3} t) = - \frac{9}{40}

cos (\frac{2 π}{3} t) = - \frac{9}{40}

Aplicar propiedades trigonométricas inversas

cos (\frac{2 π}{3} t) = - \frac{9}{40}

Soluciones generales para

cos (\frac{2 π}{3} t) = - \frac{9}{40}

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

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn, \frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn, \frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn

Resolver

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn : t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn

Multiplicar ambos lados por

3

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn

Multiplicar ambos lados por

3

3 \cdot \frac{2 π}{3} t = 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{2 π}{3} t = 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{2 π}{3} t : 2 π t

3 \cdot \frac{2 π}{3} t

Multiplicar fracciones:

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

= \frac{2 \cdot 3 π}{3} t

Eliminar los terminos comunes:

3

= t \cdot 2 π

Simplificar

3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn : 3 arccos (- \frac{9}{40}) + 6 πn

3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = 3 arccos (- \frac{9}{40}) + 6 πn

Dividir ambos lados entre

2 π

2 π t = 3 arccos (- \frac{9}{40}) + 6 πn

Dividir ambos lados entre

2 π

\frac{2 π t}{2 π} = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 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{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π} : \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

\frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Cancelar

\frac{6 πn}{2 π} : 3 n

\frac{6 πn}{2 π}

Cancelar

\frac{6 πn}{2 π} : 3 n

\frac{6 πn}{2 π}

Dividir:

\frac{6}{2} = 3

= \frac{3 πn}{π}

Eliminar los terminos comunes:

π

= 3 n

= 3 n

= \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

Resolver

\frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn : t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

\frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn

Multiplicar ambos lados por

3

\frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn

Multiplicar ambos lados por

3

3 \cdot \frac{2 π}{3} t = - 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{2 π}{3} t = - 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{2 π}{3} t : 2 π t

3 \cdot \frac{2 π}{3} t

Multiplicar fracciones:

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

= \frac{2 \cdot 3 π}{3} t

Eliminar los terminos comunes:

3

= t \cdot 2 π

Simplificar

- 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn : - 3 arccos (- \frac{9}{40}) + 6 πn

- 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Multiplicar los numeros:

3 \cdot 2 = 6

= - 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = - 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = - 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = - 3 arccos (- \frac{9}{40}) + 6 πn

Dividir ambos lados entre

2 π

2 π t = - 3 arccos (- \frac{9}{40}) + 6 πn

Dividir ambos lados entre

2 π

\frac{2 π t}{2 π} = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 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{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π} : - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

- \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Cancelar

\frac{6 πn}{2 π} : 3 n

\frac{6 πn}{2 π}

Cancelar

\frac{6 πn}{2 π} : 3 n

\frac{6 πn}{2 π}

Dividir:

\frac{6}{2} = 3

= \frac{3 πn}{π}

Eliminar los terminos comunes:

π

= 3 n

= 3 n

= - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n, t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

Mostrar soluciones en forma decimal

t = \frac{3 \cdot 1.79773 \dots}{2 π} + 3 n, t = - \frac{3 \cdot 1.79773 \dots}{2 π} + 3 n

Gráfica

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