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Popular >

0=-(sin(6.9256-x)+(sin(-x)))

Solución

0 = - (sin (6.9256 - x) + (sin (- x)))

Solución

x = - 2 πn + \frac{6.9256}{2}, x = - π + \frac{6.9256}{2} - 2 πn

Grados

x = 198.40382 \dots^{\circ} - 36 0^{\circ} n, x = 18.40382 \dots^{\circ} - 36 0^{\circ} n

Pasos de solución

0 = - (sin (6.9256 - x) + (sin (- x)))

Intercambiar lados

- (sin (6.9256 - x) + sin (- x)) = 0

Re-escribir usando identidades trigonométricas

- (sin (6.9256 - x) + sin (- x))

Utilizar la identidad suma-producto:

sin (s) + sin (t) = 2 sin (\frac{s + t}{2}) cos (\frac{s - t}{2})

= - 2 sin (\frac{6.9256 - x - x}{2}) cos (\frac{6.9256 - x - ( - x )}{2})

Simplificar

- 2 sin (\frac{6.9256 - x - x}{2}) cos (\frac{6.9256 - x - ( - x )}{2}) : 1.89770 \dots sin (\frac{6.9256 - 2 x}{2})

- 2 sin (\frac{6.9256 - x - x}{2}) cos (\frac{6.9256 - x - ( - x )}{2})

Aplicar la regla

- (- a) = a

= - 2 sin (\frac{- x - x + 6.9256}{2}) cos (\frac{x - x + 6.9256}{2})

Sumar elementos similares:

- x - x = - 2 x

= - 2 sin (\frac{- 2 x + 6.9256}{2}) cos (\frac{x - x + 6.9256}{2})

Sumar elementos similares:

- x + x = 0

= - 2 cos (\frac{6.9256}{2}) sin (\frac{- 2 x + 6.9256}{2})

Dividir:

\frac{6.9256}{2} = 3.4628

= - 2 cos (3.4628) sin (\frac{- 2 x + 6.9256}{2})

Simplificar

cos (3.4628) : - 0.94885 \dots

cos (3.4628)

cos (3.4628) = - 0.94885 \dots

= - 0.94885 \dots

= - 2 (- 0.94885 \dots) sin (\frac{- 2 x + 6.9256}{2})

Simplificar

= 1.89770 \dots sin (\frac{- 2 x + 6.9256}{2})

= 1.89770 \dots sin (\frac{6.9256 - 2 x}{2})

1.89770 \dots sin (\frac{6.9256 - 2 x}{2}) = 0

Dividir ambos lados entre

1.89770 \dots

1.89770 \dots sin (\frac{6.9256 - 2 x}{2}) = 0

Dividir ambos lados entre

1.89770 \dots

\frac{1.89770 \dots sin ( \frac{6.9256 - 2 x}{2} )}{1.89770 \dots} = \frac{0}{1.89770 \dots}

Simplificar

sin (\frac{6.9256 - 2 x}{2}) = 0

sin (\frac{6.9256 - 2 x}{2}) = 0

Soluciones generales para

sin (\frac{6.9256 - 2 x}{2}) = 0

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{6.9256 - 2 x}{2} = 0 + 2 πn, \frac{6.9256 - 2 x}{2} = π + 2 πn

\frac{6.9256 - 2 x}{2} = 0 + 2 πn, \frac{6.9256 - 2 x}{2} = π + 2 πn

Resolver

\frac{6.9256 - 2 x}{2} = 0 + 2 πn : x = - 2 πn + \frac{6.9256}{2}

\frac{6.9256 - 2 x}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{6.9256 - 2 x}{2} = 2 πn

Multiplicar ambos lados por

2

\frac{6.9256 - 2 x}{2} = 2 πn

Multiplicar ambos lados por

2

\frac{2 ( 6.9256 - 2 x )}{2} = 2 \cdot 2 πn

Simplificar

6.9256 - 2 x = 4 πn

6.9256 - 2 x = 4 πn

Mover

6.9256

al lado derecho

6.9256 - 2 x = 4 πn

Restar

6.9256

de ambos lados

6.9256 - 2 x - 6.9256 = 4 πn - 6.9256

Simplificar

- 2 x = 4 πn - 6.9256

- 2 x = 4 πn - 6.9256

Dividir ambos lados entre

- 2

- 2 x = 4 πn - 6.9256

Dividir ambos lados entre

- 2

\frac{- 2 x}{- 2} = \frac{4 πn}{- 2} - \frac{6.9256}{- 2}

Simplificar

\frac{- 2 x}{- 2} = \frac{4 πn}{- 2} - \frac{6.9256}{- 2}

Simplificar

\frac{- 2 x}{- 2} : x

\frac{- 2 x}{- 2}

Aplicar las propiedades de las fracciones:

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

= \frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{4 πn}{- 2} - \frac{6.9256}{- 2} : - 2 πn + \frac{6.9256}{2}

\frac{4 πn}{- 2} - \frac{6.9256}{- 2}

\frac{4 πn}{- 2} = - 2 πn

\frac{4 πn}{- 2}

Aplicar las propiedades de las fracciones:

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

= - \frac{4 πn}{2}

Dividir:

\frac{4}{2} = 2

= - 2 πn

= - 2 πn - \frac{6.9256}{- 2}

Aplicar las propiedades de las fracciones:

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

= - 2 πn - (- \frac{6.9256}{2})

Aplicar la regla

- (- a) = a

= - 2 πn + \frac{6.9256}{2}

x = - 2 πn + \frac{6.9256}{2}

x = - 2 πn + \frac{6.9256}{2}

x = - 2 πn + \frac{6.9256}{2}

Resolver

\frac{6.9256 - 2 x}{2} = π + 2 πn : x = - π + \frac{6.9256}{2} - 2 πn

\frac{6.9256 - 2 x}{2} = π + 2 πn

Multiplicar ambos lados por

2

\frac{6.9256 - 2 x}{2} = π + 2 πn

Multiplicar ambos lados por

2

\frac{2 ( 6.9256 - 2 x )}{2} = 2 π + 2 \cdot 2 πn

Simplificar

6.9256 - 2 x = 2 π + 4 πn

6.9256 - 2 x = 2 π + 4 πn

Mover

6.9256

al lado derecho

6.9256 - 2 x = 2 π + 4 πn

Restar

6.9256

de ambos lados

6.9256 - 2 x - 6.9256 = 2 π + 4 πn - 6.9256

Simplificar

- 2 x = 2 π + 4 πn - 6.9256

- 2 x = 2 π + 4 πn - 6.9256

Dividir ambos lados entre

- 2

- 2 x = 2 π + 4 πn - 6.9256

Dividir ambos lados entre

- 2

\frac{- 2 x}{- 2} = \frac{2 π}{- 2} + \frac{4 πn}{- 2} - \frac{6.9256}{- 2}

Simplificar

\frac{- 2 x}{- 2} = \frac{2 π}{- 2} + \frac{4 πn}{- 2} - \frac{6.9256}{- 2}

Simplificar

\frac{- 2 x}{- 2} : x

\frac{- 2 x}{- 2}

Aplicar las propiedades de las fracciones:

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

= \frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{2 π}{- 2} + \frac{4 πn}{- 2} - \frac{6.9256}{- 2} : - π + \frac{6.9256}{2} - 2 πn

\frac{2 π}{- 2} + \frac{4 πn}{- 2} - \frac{6.9256}{- 2}

Agrupar términos semejantes

= \frac{2 π}{- 2} - \frac{6.9256}{- 2} + \frac{4 πn}{- 2}

\frac{2 π}{- 2} = - π

\frac{2 π}{- 2}

Aplicar las propiedades de las fracciones:

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

= - \frac{2 π}{2}

Dividir:

\frac{2}{2} = 1

= - π

= - π - \frac{6.9256}{- 2} + \frac{4 πn}{- 2}

\frac{6.9256}{- 2} = - \frac{6.9256}{2}

\frac{6.9256}{- 2}

Aplicar las propiedades de las fracciones:

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

= - \frac{6.9256}{2}

\frac{4 πn}{- 2} = - 2 πn

\frac{4 πn}{- 2}

Aplicar las propiedades de las fracciones:

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

= - \frac{4 πn}{2}

Dividir:

\frac{4}{2} = 2

= - 2 πn

= - π - (- \frac{6.9256}{2}) - 2 πn

Aplicar la regla

- (- a) = a

= - π + \frac{6.9256}{2} - 2 πn

x = - π + \frac{6.9256}{2} - 2 πn

x = - π + \frac{6.9256}{2} - 2 πn

x = - π + \frac{6.9256}{2} - 2 πn

x = - 2 πn + \frac{6.9256}{2}, x = - π + \frac{6.9256}{2} - 2 πn

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