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Popular >

15=-40sin(18(x-10))

Solución

15 = - 40 sin (18 (x - 10))

Solución

x = - \frac{0.38439 \dots}{18} + \frac{πn}{9} + 10, x = \frac{π + 0.38439 \dots}{18} + \frac{πn}{9} + 10

Grados

x = 571.73422 \dots^{\circ} + 2 0^{\circ} n, x = 584.18136 \dots^{\circ} + 2 0^{\circ} n

Pasos de solución

15 = - 40 sin (18 (x - 10))

Intercambiar lados

- 40 sin (18 (x - 10)) = 15

Dividir ambos lados entre

- 40

- 40 sin (18 (x - 10)) = 15

Dividir ambos lados entre

- 40

\frac{- 40 sin ( 18 ( x - 10 ) )}{- 40} = \frac{15}{- 40}

Simplificar

\frac{- 40 sin ( 18 ( x - 10 ) )}{- 40} = \frac{15}{- 40}

Simplificar

\frac{- 40 sin ( 18 ( x - 10 ) )}{- 40} : sin (18 (x - 10))

\frac{- 40 sin ( 18 ( x - 10 ) )}{- 40}

Aplicar las propiedades de las fracciones:

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

= \frac{40 sin ( 18 ( x - 10 ) )}{40}

Dividir:

\frac{40}{40} = 1

= sin (18 (x - 10))

Simplificar

\frac{15}{- 40} : - \frac{3}{8}

\frac{15}{- 40}

Aplicar las propiedades de las fracciones:

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

= - \frac{15}{40}

Eliminar los terminos comunes:

5

= - \frac{3}{8}

sin (18 (x - 10)) = - \frac{3}{8}

sin (18 (x - 10)) = - \frac{3}{8}

sin (18 (x - 10)) = - \frac{3}{8}

Aplicar propiedades trigonométricas inversas

sin (18 (x - 10)) = - \frac{3}{8}

Soluciones generales para

sin (18 (x - 10)) = - \frac{3}{8}

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

18 (x - 10) = arcsin (- \frac{3}{8}) + 2 πn, 18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn

18 (x - 10) = arcsin (- \frac{3}{8}) + 2 πn, 18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn

Resolver

18 (x - 10) = arcsin (- \frac{3}{8}) + 2 πn : x = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

18 (x - 10) = arcsin (- \frac{3}{8}) + 2 πn

Simplificar

arcsin (- \frac{3}{8}) + 2 πn : - arcsin (\frac{3}{8}) + 2 πn

arcsin (- \frac{3}{8}) + 2 πn

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{8}) = - arcsin (\frac{3}{8})

= - arcsin (\frac{3}{8}) + 2 πn

18 (x - 10) = - arcsin (\frac{3}{8}) + 2 πn

Dividir ambos lados entre

18

18 (x - 10) = - arcsin (\frac{3}{8}) + 2 πn

Dividir ambos lados entre

18

\frac{18 ( x - 10 )}{18} = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{2 πn}{18}

Simplificar

x - 10 = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

x - 10 = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

Mover

10

al lado derecho

x - 10 = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

Sumar

10

a ambos lados

x - 10 + 10 = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Simplificar

x = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Resolver

18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn : x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn

Dividir ambos lados entre

18

18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn

Dividir ambos lados entre

18

\frac{18 ( x - 10 )}{18} = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{2 πn}{18}

Simplificar

x - 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

x - 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

Mover

10

al lado derecho

x - 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

Sumar

10

a ambos lados

x - 10 + 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Simplificar

x - 10 + 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Simplificar

x - 10 + 10 : x

x - 10 + 10

Sumar elementos similares:

- 10 + 10 = 0

= x

Simplificar

\frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10 : \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

\frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Combinar las fracciones usando el mínimo común denominador:

\frac{π + arcsin ( \frac{3}{8} )}{18}

Aplicar la regla

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

= \frac{π + arcsin ( \frac{3}{8} )}{18}

= \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10, x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Mostrar soluciones en forma decimal

x = - \frac{0.38439 \dots}{18} + \frac{πn}{9} + 10, x = \frac{π + 0.38439 \dots}{18} + \frac{πn}{9} + 10

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