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Popular Trigonometría >

950sin(pi/6 (7-x))+1650=2500

Solución

950 sin (\frac{π}{6} (7 - x)) + 1650 = 2500

Solución

x = 7 - 12 n - \frac{6 \cdot 1.10784 \dots}{π}, x = - 12 n + 1 + \frac{6 \cdot 1.10784 \dots}{π}

Grados

x = 279.84280 \dots^{\circ} - 687.54935 \dots^{\circ} n, x = 178.52342 \dots^{\circ} - 687.54935 \dots^{\circ} n

Pasos de solución

950 sin (\frac{π}{6} (7 - x)) + 1650 = 2500

Desplace

1650

a la derecha

950 sin (\frac{π}{6} (7 - x)) + 1650 = 2500

Restar

1650

de ambos lados

950 sin (\frac{π}{6} (7 - x)) + 1650 - 1650 = 2500 - 1650

Simplificar

950 sin (\frac{π}{6} (7 - x)) = 850

950 sin (\frac{π}{6} (7 - x)) = 850

Dividir ambos lados entre

950

950 sin (\frac{π}{6} (7 - x)) = 850

Dividir ambos lados entre

950

\frac{950 sin ( \frac{π}{6} ( 7 - x ) )}{950} = \frac{850}{950}

Simplificar

sin (\frac{π}{6} (7 - x)) = \frac{17}{19}

sin (\frac{π}{6} (7 - x)) = \frac{17}{19}

Aplicar propiedades trigonométricas inversas

sin (\frac{π}{6} (7 - x)) = \frac{17}{19}

Soluciones generales para

sin (\frac{π}{6} (7 - x)) = \frac{17}{19}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn, \frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn, \frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn

Resolver

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn : x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn

Multiplicar ambos lados por

6

\frac{π}{6} (7 - x) = arcsin (\frac{17}{19}) + 2 πn

Multiplicar ambos lados por

6

6 \cdot \frac{π}{6} (7 - x) = 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (7 - x) = 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (7 - x) : π (7 - x)

6 \cdot \frac{π}{6} (7 - x)

Multiplicar fracciones:

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

= \frac{6 π}{6} (- x + 7)

Eliminar los terminos comunes:

6

= (7 - x) π

Simplificar

6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn : 6 arcsin (\frac{17}{19}) + 12 πn

6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 arcsin (\frac{17}{19}) + 12 πn

Dividir ambos lados entre

π

π (7 - x) = 6 arcsin (\frac{17}{19}) + 12 πn

Dividir ambos lados entre

π

\frac{π ( 7 - x )}{π} = \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Simplificar

7 - x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

7 - x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

Desplace

7

a la derecha

7 - x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

Restar

7

de ambos lados

7 - x - 7 = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Simplificar

- x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

- x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Dividir ambos lados entre

- 1

- x = \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Dividir ambos lados entre

- 1

\frac{- x}{- 1} = \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} + \frac{12 n}{- 1} - \frac{7}{- 1}

Simplificar

\frac{- x}{- 1} = \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} + \frac{12 n}{- 1} - \frac{7}{- 1}

Simplificar

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Aplicar las propiedades de las fracciones:

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

= \frac{x}{1}

Aplicar la regla

\frac{a}{1} = a

= x

Simplificar

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} + \frac{12 n}{- 1} - \frac{7}{- 1} : 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} + \frac{12 n}{- 1} - \frac{7}{- 1}

Agrupar términos semejantes

= - \frac{7}{- 1} + \frac{12 n}{- 1} + \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

\frac{7}{- 1} = - 7

\frac{7}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{7}{1}

Aplicar la regla

\frac{a}{1} = a

= - 7

\frac{12 n}{- 1} = - 12 n

\frac{12 n}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{12 n}{1}

Aplicar la regla

\frac{a}{1} = a

= - 12 n

= - (- 7) - 12 n + \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Aplicar la regla

- (- a) = a

= 7 - 12 n + \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} = - \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{1} = \frac{6 arcsin ( \frac{17}{19} )}{π}

= - \frac{6 arcsin ( \frac{17}{19} )}{π}

= 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}

Resolver

\frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn : x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn

Multiplicar ambos lados por

6

\frac{π}{6} (7 - x) = π - arcsin (\frac{17}{19}) + 2 πn

Multiplicar ambos lados por

6

6 \cdot \frac{π}{6} (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Simplificar

6 \cdot \frac{π}{6} (7 - x) : π (7 - x)

6 \cdot \frac{π}{6} (7 - x)

Multiplicar fracciones:

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

= \frac{6 π}{6} (- x + 7)

Eliminar los terminos comunes:

6

= (7 - x) π

Simplificar

6 π - 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn : 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

6 π - 6 arcsin (\frac{17}{19}) + 6 \cdot 2 πn

Multiplicar los numeros:

6 \cdot 2 = 12

= 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

π (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

Dividir ambos lados entre

π

π (7 - x) = 6 π - 6 arcsin (\frac{17}{19}) + 12 πn

Dividir ambos lados entre

π

\frac{π ( 7 - x )}{π} = \frac{6 π}{π} - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Simplificar

\frac{π ( 7 - x )}{π} = \frac{6 π}{π} - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Simplificar

\frac{π ( 7 - x )}{π} : 7 - x

\frac{π ( 7 - x )}{π}

Eliminar los terminos comunes:

π

= 7 - x

Simplificar

\frac{6 π}{π} - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π} : 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

\frac{6 π}{π} - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Cancelar

\frac{6 π}{π} : 6

\frac{6 π}{π}

Eliminar los terminos comunes:

π

= 6

= 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + \frac{12 πn}{π}

Cancelar

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Eliminar los terminos comunes:

π

= 12 n

= 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

7 - x = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

7 - x = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

7 - x = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

Desplace

7

a la derecha

7 - x = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n

Restar

7

de ambos lados

7 - x - 7 = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Simplificar

7 - x - 7 = 6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Simplificar

7 - x - 7 : - x

7 - x - 7

Sumar elementos similares:

7 - 7 = 0

= - x

Simplificar

6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7 : 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

6 - \frac{6 arcsin ( \frac{17}{19} )}{π} + 12 n - 7

Restar:

6 - 7 = - 1

= 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

- x = 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

- x = 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

- x = 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

Dividir ambos lados entre

- 1

- x = 12 n - 1 - \frac{6 arcsin ( \frac{17}{19} )}{π}

Dividir ambos lados entre

- 1

\frac{- x}{- 1} = \frac{12 n}{- 1} - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Simplificar

\frac{- x}{- 1} = \frac{12 n}{- 1} - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Simplificar

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Aplicar las propiedades de las fracciones:

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

= \frac{x}{1}

Aplicar la regla

\frac{a}{1} = a

= x

Simplificar

\frac{12 n}{- 1} - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} : - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{12 n}{- 1} - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

\frac{12 n}{- 1} = - 12 n

\frac{12 n}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{12 n}{1}

Aplicar la regla

\frac{a}{1} = a

= - 12 n

= - 12 n - \frac{1}{- 1} - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

\frac{1}{- 1} = - 1

\frac{1}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{1}{1}

Aplicar la regla

\frac{a}{1} = a

= - 1

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1} = - \frac{6 arcsin ( \frac{17}{19} )}{π}

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{\frac{6 a r c s i n ( \frac{17}{19} )}{π}}{1} = \frac{6 arcsin ( \frac{17}{19} )}{π}

= - \frac{6 arcsin ( \frac{17}{19} )}{π}

= - 12 n - (- 1) - (- \frac{6 arcsin ( \frac{17}{19} )}{π})

Aplicar la regla

- (- a) = a

= - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

x = 7 - 12 n - \frac{6 arcsin ( \frac{17}{19} )}{π}, x = - 12 n + 1 + \frac{6 arcsin ( \frac{17}{19} )}{π}

Mostrar soluciones en forma decimal

x = 7 - 12 n - \frac{6 \cdot 1.10784 \dots}{π}, x = - 12 n + 1 + \frac{6 \cdot 1.10784 \dots}{π}

Gráfica

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