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(368.02)/(sin(66-x))=(290)/(sin(38))

Solución

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

Solución

x = - 36 0^{\circ} n + 6 6^{\circ} - 0.89673 \dots, x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + 0.89673 \dots

radianes

x = \frac{11 π}{30} - 0.89673 \dots - 2 πn, x = - π + \frac{11 π}{30} + 0.89673 \dots - 2 πn

Pasos de solución

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

Utilizar multiplicación cruzada (regla de tres)

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

Utilizar multiplicación cruzada (regla de tres): Si

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

entonces

a \cdot d = b \cdot c

368.02 sin (3 8^{\circ}) = sin (6 6^{\circ} - x) \cdot 290

368.02 sin (3 8^{\circ}) = sin (6 6^{\circ} - x) \cdot 290

Intercambiar lados

sin (6 6^{\circ} - x) \cdot 290 = 368.02 sin (3 8^{\circ})

Dividir ambos lados entre

290

sin (6 6^{\circ} - x) \cdot 290 = 368.02 sin (3 8^{\circ})

Dividir ambos lados entre

290

\frac{sin ( 6 6 ^{\circ} - x ) \cdot 290}{290} = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

Simplificar

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

Verificar las soluciones

Encontrar los puntos no definidos (singularidades):

sin (6 6^{\circ} - x) = 0

Tomar el(los) denominador(es) de

\frac{368.02}{sin ( 6 6 ^{\circ} - x )}

y comparar con cero

sin (6 6^{\circ} - x) = 0

Los siguientes puntos no están definidos

sin (6 6^{\circ} - x) = 0

Combinar los puntos no definidos con las soluciones:

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

Aplicar propiedades trigonométricas inversas

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

Soluciones generales para

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n, 6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n, 6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

Resolver

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n : x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

Mover

6 6^{\circ}

al lado derecho

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

Restar

6 6^{\circ}

de ambos lados

6 6^{\circ} - x - 6 6^{\circ} = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

Simplificar

- x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

- x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

Dividir ambos lados entre

- 1

- x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

Dividir ambos lados entre

- 1

\frac{- x}{- 1} = \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

Simplificar

\frac{- x}{- 1} = \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 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{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1} : - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

Agrupar términos semejantes

= \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1} + \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{36 0 ^{\circ} n}{1}

Aplicar la regla

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{6 6 ^{\circ}}{- 1} + \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{6 6 ^{\circ}}{- 1} = - 6 6^{\circ}

\frac{6 6 ^{\circ}}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{6 6 ^{\circ}}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{6 6 ^{\circ}}{1} = 6 6^{\circ}

= - 6 6^{\circ}

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} = - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{1} = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

= - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

= - 36 0^{\circ} n - (- 6 6^{\circ}) - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

Aplicar la regla

- (- a) = a

= - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

Resolver

6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n : x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

Mover

6 6^{\circ}

al lado derecho

6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

Restar

6 6^{\circ}

de ambos lados

6 6^{\circ} - x - 6 6^{\circ} = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

Simplificar

- x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

- x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

Dividir ambos lados entre

- 1

- x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

Dividir ambos lados entre

- 1

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

Simplificar

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 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{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1} : - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

Agrupar términos semejantes

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

Aplicar las propiedades de las fracciones:

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

= - 18 0^{\circ}

Aplicar la regla

\frac{a}{1} = a

= - 18 0^{\circ}

= - 18 0^{\circ} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{36 0 ^{\circ} n}{1}

Aplicar la regla

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 18 0^{\circ} - 36 0^{\circ} n - \frac{6 6 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{6 6 ^{\circ}}{- 1} = - 6 6^{\circ}

\frac{6 6 ^{\circ}}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{6 6 ^{\circ}}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{6 6 ^{\circ}}{1} = 6 6^{\circ}

= - 6 6^{\circ}

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} = - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

Aplicar las propiedades de las fracciones:

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

= - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{1} = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

= - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

= - 18 0^{\circ} - 36 0^{\circ} n - (- 6 6^{\circ}) - (- arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}))

Aplicar la regla

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}), x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

Mostrar soluciones en forma decimal

x = - 36 0^{\circ} n + 6 6^{\circ} - 0.89673 \dots, x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + 0.89673 \dots

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