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Popular Trigonometría >

1.5=2.75cos(30(x-4))+3.25

Solución

1.5 = 2.75 cos (30 (x - 4)) + 3.25

Solución

x = \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4, x = - \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4

Grados

x = 233.50049 \dots^{\circ} + 1 2^{\circ} n, x = 224.86574 \dots^{\circ} + 1 2^{\circ} n

Pasos de solución

1.5 = 2.75 cos (30 (x - 4)) + 3.25

Intercambiar lados

2.75 cos (30 (x - 4)) + 3.25 = 1.5

Multiplicar ambos lados por

100

2.75 cos (30 (x - 4)) + 3.25 = 1.5

Para eliminar los puntos decimales, multiplique por 10 por cada digito después del punto decimalHay digitos

2

a la derecha del punto decimal, por lo que debe multiplicar por

100

2.75 cos (30 (x - 4)) \cdot 100 + 3.25 \cdot 100 = 1.5 \cdot 100

Simplificar

275 cos (30 (x - 4)) + 325 = 150

275 cos (30 (x - 4)) + 325 = 150

Desplace

325

a la derecha

275 cos (30 (x - 4)) + 325 = 150

Restar

325

de ambos lados

275 cos (30 (x - 4)) + 325 - 325 = 150 - 325

Simplificar

275 cos (30 (x - 4)) = - 175

275 cos (30 (x - 4)) = - 175

Dividir ambos lados entre

275

275 cos (30 (x - 4)) = - 175

Dividir ambos lados entre

275

\frac{275 cos ( 30 ( x - 4 ) )}{275} = \frac{- 175}{275}

Simplificar

\frac{275 cos ( 30 ( x - 4 ) )}{275} = \frac{- 175}{275}

Simplificar

\frac{275 cos ( 30 ( x - 4 ) )}{275} : cos (30 (x - 4))

\frac{275 cos ( 30 ( x - 4 ) )}{275}

Dividir:

\frac{275}{275} = 1

= cos (30 (x - 4))

Simplificar

\frac{- 175}{275} : - \frac{7}{11}

\frac{- 175}{275}

Aplicar las propiedades de las fracciones:

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

= - \frac{175}{275}

Eliminar los terminos comunes:

25

= - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

Aplicar propiedades trigonométricas inversas

cos (30 (x - 4)) = - \frac{7}{11}

Soluciones generales para

cos (30 (x - 4)) = - \frac{7}{11}

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

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn, 30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn, 30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

Resolver

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn : x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn

Dividir ambos lados entre

30

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn

Dividir ambos lados entre

30

\frac{30 ( x - 4 )}{30} = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{2 πn}{30}

Simplificar

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

Desplace

4

a la derecha

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

Sumar

4

a ambos lados

x - 4 + 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

Simplificar

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

Resolver

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn : x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

Dividir ambos lados entre

30

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

Dividir ambos lados entre

30

\frac{30 ( x - 4 )}{30} = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{2 πn}{30}

Simplificar

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

Desplace

4

a la derecha

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

Sumar

4

a ambos lados

x - 4 + 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

Simplificar

x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4, x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

Mostrar soluciones en forma decimal

x = \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4, x = - \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4

Gráfica

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