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csc^2(2x-0.6)=16

Solución

csc^{2} (2 x - 0.6) = 16

Solución

x = πn + \frac{0.6}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{0.25268 \dots}{2}, x = πn + \frac{0.6}{2} - \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{0.25268 \dots}{2}

Grados

x = 24.42748 \dots^{\circ} + 18 0^{\circ} n, x = 99.94997 \dots^{\circ} + 18 0^{\circ} n, x = 9.94997 \dots^{\circ} + 18 0^{\circ} n, x = 114.42748 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

csc^{2} (2 x - 0.6) = 16

Usando el método de sustitución

csc^{2} (2 x - 0.6) = 16

Sea:

csc (2 x - 0.6) = u

u^{2} = 16

u^{2} = 16 : u = 4, u = - 4

u^{2} = 16

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

u = 16, u = - 16

16 = 4

16

Descomponer el número en factores primos:

16 = 4^{2}

= 4^{2}

Aplicar las leyes de los exponentes:

4^{2} = 4

= 4

- 16 = - 4

- 16

16 = 4

16

Descomponer el número en factores primos:

16 = 4^{2}

= 4^{2}

Aplicar las leyes de los exponentes:

4^{2} = 4

= 4

= - 4

u = 4, u = - 4

Sustituir en la ecuación

u = csc (2 x - 0.6)

csc (2 x - 0.6) = 4, csc (2 x - 0.6) = - 4

csc (2 x - 0.6) = 4, csc (2 x - 0.6) = - 4

csc (2 x - 0.6) = 4 : x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

csc (2 x - 0.6) = 4

Aplicar propiedades trigonométricas inversas

csc (2 x - 0.6) = 4

Soluciones generales para

csc (2 x - 0.6) = 4

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

2 x - 0.6 = arccsc (4) + 2 πn, 2 x - 0.6 = π - arccsc (4) + 2 πn

2 x - 0.6 = arccsc (4) + 2 πn, 2 x - 0.6 = π - arccsc (4) + 2 πn

Resolver

2 x - 0.6 = arccsc (4) + 2 πn : x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

2 x - 0.6 = arccsc (4) + 2 πn

Mover

0.6

al lado derecho

2 x - 0.6 = arccsc (4) + 2 πn

Sumar

0.6

a ambos lados

2 x - 0.6 + 0.6 = arccsc (4) + 2 πn + 0.6

Simplificar

2 x = arccsc (4) + 2 πn + 0.6

2 x = arccsc (4) + 2 πn + 0.6

Dividir ambos lados entre

2

2 x = arccsc (4) + 2 πn + 0.6

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Simplificar

\frac{2 x}{2} = \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2} : πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

\frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Agrupar términos semejantes

= \frac{0.6}{2} + \frac{2 πn}{2} + \frac{arccsc ( 4 )}{2}

Dividir:

\frac{2}{2} = 1

= \frac{0.6}{2} + πn + \frac{arccsc ( 4 )}{2}

Agrupar términos semejantes

= πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

Resolver

2 x - 0.6 = π - arccsc (4) + 2 πn : x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

2 x - 0.6 = π - arccsc (4) + 2 πn

Mover

0.6

al lado derecho

2 x - 0.6 = π - arccsc (4) + 2 πn

Sumar

0.6

a ambos lados

2 x - 0.6 + 0.6 = π - arccsc (4) + 2 πn + 0.6

Simplificar

2 x = π - arccsc (4) + 2 πn + 0.6

2 x = π - arccsc (4) + 2 πn + 0.6

Dividir ambos lados entre

2

2 x = π - arccsc (4) + 2 πn + 0.6

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Simplificar

\frac{2 x}{2} = \frac{π}{2} - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{π}{2} - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2} : πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

\frac{π}{2} - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Agrupar términos semejantes

= \frac{π}{2} + \frac{0.6}{2} + \frac{2 πn}{2} - \frac{arccsc ( 4 )}{2}

Dividir:

\frac{2}{2} = 1

= \frac{π}{2} + \frac{0.6}{2} + πn - \frac{arccsc ( 4 )}{2}

Agrupar términos semejantes

= πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

csc (2 x - 0.6) = - 4 : x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

csc (2 x - 0.6) = - 4

Aplicar propiedades trigonométricas inversas

csc (2 x - 0.6) = - 4

Soluciones generales para

csc (2 x - 0.6) = - 4

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

2 x - 0.6 = arccsc (- 4) + 2 πn, 2 x - 0.6 = π + arccsc (4) + 2 πn

2 x - 0.6 = arccsc (- 4) + 2 πn, 2 x - 0.6 = π + arccsc (4) + 2 πn

Resolver

2 x - 0.6 = arccsc (- 4) + 2 πn : x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

2 x - 0.6 = arccsc (- 4) + 2 πn

Simplificar

arccsc (- 4) + 2 πn : - arccsc (4) + 2 πn

arccsc (- 4) + 2 πn

Utilizar la siguiente propiedad:

arccsc (- x) = - arccsc (x)

arccsc (- 4) = - arccsc (4)

= - arccsc (4) + 2 πn

2 x - 0.6 = - arccsc (4) + 2 πn

Mover

0.6

al lado derecho

2 x - 0.6 = - arccsc (4) + 2 πn

Sumar

0.6

a ambos lados

2 x - 0.6 + 0.6 = - arccsc (4) + 2 πn + 0.6

Simplificar

2 x = - arccsc (4) + 2 πn + 0.6

2 x = - arccsc (4) + 2 πn + 0.6

Dividir ambos lados entre

2

2 x = - arccsc (4) + 2 πn + 0.6

Dividir ambos lados entre

2

\frac{2 x}{2} = - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Simplificar

\frac{2 x}{2} = - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

- \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2} : πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

- \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Agrupar términos semejantes

= \frac{0.6}{2} + \frac{2 πn}{2} - \frac{arccsc ( 4 )}{2}

Dividir:

\frac{2}{2} = 1

= \frac{0.6}{2} + πn - \frac{arccsc ( 4 )}{2}

Agrupar términos semejantes

= πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

Resolver

2 x - 0.6 = π + arccsc (4) + 2 πn : x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

2 x - 0.6 = π + arccsc (4) + 2 πn

Mover

0.6

al lado derecho

2 x - 0.6 = π + arccsc (4) + 2 πn

Sumar

0.6

a ambos lados

2 x - 0.6 + 0.6 = π + arccsc (4) + 2 πn + 0.6

Simplificar

2 x = π + arccsc (4) + 2 πn + 0.6

2 x = π + arccsc (4) + 2 πn + 0.6

Dividir ambos lados entre

2

2 x = π + arccsc (4) + 2 πn + 0.6

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Simplificar

\frac{2 x}{2} = \frac{π}{2} + \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{π}{2} + \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2} : πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

\frac{π}{2} + \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

Agrupar términos semejantes

= \frac{π}{2} + \frac{0.6}{2} + \frac{2 πn}{2} + \frac{arccsc ( 4 )}{2}

Dividir:

\frac{2}{2} = 1

= \frac{π}{2} + \frac{0.6}{2} + πn + \frac{arccsc ( 4 )}{2}

Agrupar términos semejantes

= πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

Combinar toda las soluciones

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}, x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

Mostrar soluciones en forma decimal

x = πn + \frac{0.6}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{0.25268 \dots}{2}, x = πn + \frac{0.6}{2} - \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{0.25268 \dots}{2}

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