English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-11cos(x)22-11sin(x)8=-250

Solución

- 11 cos (x) 22 - 11 sin (x) 8 = - 250

Solución

x = 0.10677 \dots + 2 πn, x = 0.59076 \dots + 2 πn

Grados

x = 6.11761 \dots^{\circ} + 36 0^{\circ} n, x = 33.84860 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

- 11 cos (x) \cdot 22 - 11 sin (x) \cdot 8 = - 250

Sumar

11 sin (x) 8

a ambos lados

- 242 cos (x) = - 250 + 88 sin (x)

Elevar al cuadrado ambos lados

(- 242 cos (x))^{2} = (- 250 + 88 sin (x))^{2}

Restar

(- 250 + 88 sin (x))^{2}

de ambos lados

58564 cos^{2} (x) - 62500 + 44000 sin (x) - 7744 sin^{2} (x) = 0

Re-escribir usando identidades trigonométricas

- 62500 + 44000 sin (x) + 58564 cos^{2} (x) - 7744 sin^{2} (x)

Utilizar la identidad pitagórica:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= - 62500 + 44000 sin (x) + 58564 (1 - sin^{2} (x)) - 7744 sin^{2} (x)

Simplificar

- 62500 + 44000 sin (x) + 58564 (1 - sin^{2} (x)) - 7744 sin^{2} (x) : 44000 sin (x) - 66308 sin^{2} (x) - 3936

- 62500 + 44000 sin (x) + 58564 (1 - sin^{2} (x)) - 7744 sin^{2} (x)

Expandir

58564 (1 - sin^{2} (x)) : 58564 - 58564 sin^{2} (x)

58564 (1 - sin^{2} (x))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 58564, b = 1, c = sin^{2} (x)

= 58564 \cdot 1 - 58564 sin^{2} (x)

Multiplicar los numeros:

58564 \cdot 1 = 58564

= 58564 - 58564 sin^{2} (x)

= - 62500 + 44000 sin (x) + 58564 - 58564 sin^{2} (x) - 7744 sin^{2} (x)

Simplificar

- 62500 + 44000 sin (x) + 58564 - 58564 sin^{2} (x) - 7744 sin^{2} (x) : 44000 sin (x) - 66308 sin^{2} (x) - 3936

- 62500 + 44000 sin (x) + 58564 - 58564 sin^{2} (x) - 7744 sin^{2} (x)

Sumar elementos similares:

- 58564 sin^{2} (x) - 7744 sin^{2} (x) = - 66308 sin^{2} (x)

= - 62500 + 44000 sin (x) + 58564 - 66308 sin^{2} (x)

Agrupar términos semejantes

= 44000 sin (x) - 66308 sin^{2} (x) - 62500 + 58564

Sumar/restar lo siguiente:

- 62500 + 58564 = - 3936

= 44000 sin (x) - 66308 sin^{2} (x) - 3936

= 44000 sin (x) - 66308 sin^{2} (x) - 3936

= 44000 sin (x) - 66308 sin^{2} (x) - 3936

- 3936 + 44000 sin (x) - 66308 sin^{2} (x) = 0

Usando el método de sustitución

- 3936 + 44000 sin (x) - 66308 sin^{2} (x) = 0

Sea:

sin (x) = u

- 3936 + 44000 u - 66308 u^{2} = 0

- 3936 + 44000 u - 66308 u^{2} = 0 : u = \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}, u = \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

- 3936 + 44000 u - 66308 u^{2} = 0

Escribir en la forma binómica

a x^{2} + b x + c = 0

- 66308 u^{2} + 44000 u - 3936 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

- 66308 u^{2} + 44000 u - 3936 = 0

Formula general para ecuaciones de segundo grado:

Para

a = - 66308, b = 44000, c = - 3936

u_{1, 2} = \frac{- 44000 \pm 4400 0 ^{2} - 4 ( - 66308 ) ( - 3936 )}{2 ( - 66308 )}

u_{1, 2} = \frac{- 44000 \pm 4400 0 ^{2} - 4 ( - 66308 ) ( - 3936 )}{2 ( - 66308 )}

4400 0^{2} - 4 (- 66308) (- 3936) = 4400 0^{2} - 1043953152

4400 0^{2} - 4 (- 66308) (- 3936)

Aplicar la regla

- (- a) = a

= 4400 0^{2} - 4 \cdot 66308 \cdot 3936

Multiplicar los numeros:

4 \cdot 66308 \cdot 3936 = 1043953152

= 4400 0^{2} - 1043953152

u_{1, 2} = \frac{- 44000 \pm 4400 0 ^{2} - 1043953152}{2 ( - 66308 )}

Separar las soluciones

u_{1} = \frac{- 44000 + 4400 0 ^{2} - 1043953152}{2 ( - 66308 )}, u_{2} = \frac{- 44000 - 4400 0 ^{2} - 1043953152}{2 ( - 66308 )}

u = \frac{- 44000 + 4400 0 ^{2} - 1043953152}{2 ( - 66308 )} : \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}

\frac{- 44000 + 4400 0 ^{2} - 1043953152}{2 ( - 66308 )}

Quitar los parentesis:

(- a) = - a

= \frac{- 44000 + 4400 0 ^{2} - 1043953152}{- 2 \cdot 66308}

Multiplicar los numeros:

2 \cdot 66308 = 132616

= \frac{- 44000 + 4400 0 ^{2} - 1043953152}{- 132616}

Aplicar las propiedades de las fracciones:

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

- 44000 + 4400 0^{2} - 1043953152 = - (- 4400 0^{2} - 1043953152 + 44000)

= \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}

u = \frac{- 44000 - 4400 0 ^{2} - 1043953152}{2 ( - 66308 )} : \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

\frac{- 44000 - 4400 0 ^{2} - 1043953152}{2 ( - 66308 )}

Quitar los parentesis:

(- a) = - a

= \frac{- 44000 - 4400 0 ^{2} - 1043953152}{- 2 \cdot 66308}

Multiplicar los numeros:

2 \cdot 66308 = 132616

= \frac{- 44000 - 4400 0 ^{2} - 1043953152}{- 132616}

Aplicar las propiedades de las fracciones:

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

- 44000 - 4400 0^{2} - 1043953152 = - (4400 0^{2} - 1043953152 + 44000)

= \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

Las soluciones a la ecuación de segundo grado son:

u = \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}, u = \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

Sustituir en la ecuación

u = sin (x)

sin (x) = \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}, sin (x) = \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

sin (x) = \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}, sin (x) = \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

sin (x) = \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616} : x = arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

sin (x) = \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}

Soluciones generales para

sin (x) = \frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}

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

x = arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

x = arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

sin (x) = \frac{4400 0 ^{2} - 1043953152 + 44000}{132616} : x = arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

sin (x) = \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

Soluciones generales para

sin (x) = \frac{4400 0 ^{2} - 1043953152 + 44000}{132616}

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

x = arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

x = arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

Combinar toda las soluciones

x = arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

Verificar las soluciones sustituyendo en la ecuación original

Verificar las soluciones sustituyéndolas en

- 11 cos (x) 22 - 11 sin (x) 8 = - 250

Quitar las que no concuerden con la ecuación.

Verificar la solución

arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn :

Verdadero

arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

Sustituir

n = 1

arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1

Multiplicar

- 11 cos (x) 22 - 11 sin (x) 8 = - 250

por

x = arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1

- 11 cos (arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1) \cdot 22 - 11 sin (arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1) \cdot 8 = - 250

Simplificar

- 250 = - 250

\Rightarrow Verdadero

Verificar la solución

π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn :

Falso

π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

Sustituir

n = 1

π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1

Multiplicar

- 11 cos (x) 22 - 11 sin (x) 8 = - 250

por

x = π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1

- 11 cos (π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1) \cdot 22 - 11 sin (π - arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1) \cdot 8 = - 250

Simplificar

231.24373 \dots = - 250

\Rightarrow Falso

Verificar la solución

arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn :

Verdadero

arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

Sustituir

n = 1

arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1

Multiplicar

- 11 cos (x) 22 - 11 sin (x) 8 = - 250

por

x = arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1

- 11 cos (arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1) \cdot 22 - 11 sin (arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1) \cdot 8 = - 250

Simplificar

- 250 = - 250

\Rightarrow Verdadero

Verificar la solución

π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn :

Falso

π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

Sustituir

n = 1

π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1

Multiplicar

- 11 cos (x) 22 - 11 sin (x) 8 = - 250

por

x = π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1

- 11 cos (π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1) \cdot 22 - 11 sin (π - arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 π 1) \cdot 8 = - 250

Simplificar

151.96794 \dots = - 250

\Rightarrow Falso

x = arcsin (\frac{- 4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn, x = arcsin (\frac{4400 0 ^{2} - 1043953152 + 44000}{132616}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.10677 \dots + 2 πn, x = 0.59076 \dots + 2 πn

Ejemplos populares

(sin(53.3))/(20.7)=(sin(x))/(24.9)

\frac{sin ( 53. 3 ^{\circ} )}{20.7} = \frac{sin ( x )}{24.9}

solvefor c,1=pi(0)-0arccos(ln(0)+c)resolver para

c, 1 = π (0) - 0 arccos (ln (0) + c)

solvefor θ,a(1+cos(θ))=0 resolver para

θ, a (1 + cos (θ)) = 0

cos(θ)= 1/(sqrt(21))

cos (θ) = \frac{1}{21}

-1/(sqrt(2))=cos(x)

- \frac{1}{2} = cos (x)