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Popular >

8sin(8x)+9=3

Solución

8 sin (8 x) + 9 = 3

Solución

x = - \frac{0.84806 \dots}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{0.84806 \dots}{8} + \frac{πn}{4}

+1

Grados

x = - 6.07379 \dots^{\circ} + 4 5^{\circ} n, x = 28.57379 \dots^{\circ} + 4 5^{\circ} n

Pasos de solución

8 sin (8 x) + 9 = 3

Mover

9

al lado derecho

8 sin (8 x) + 9 = 3

Restar

9

de ambos lados

8 sin (8 x) + 9 - 9 = 3 - 9

Simplificar

8 sin (8 x) = - 6

8 sin (8 x) = - 6

Dividir ambos lados entre

8

8 sin (8 x) = - 6

Dividir ambos lados entre

8

\frac{8 sin ( 8 x )}{8} = \frac{- 6}{8}

Simplificar

\frac{8 sin ( 8 x )}{8} = \frac{- 6}{8}

Simplificar

\frac{8 sin ( 8 x )}{8} : sin (8 x)

\frac{8 sin ( 8 x )}{8}

Dividir:

\frac{8}{8} = 1

= sin (8 x)

Simplificar

\frac{- 6}{8} : - \frac{3}{4}

\frac{- 6}{8}

Aplicar las propiedades de las fracciones:

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

= - \frac{6}{8}

Eliminar los terminos comunes:

2

= - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

Aplicar propiedades trigonométricas inversas

sin (8 x) = - \frac{3}{4}

Soluciones generales para

sin (8 x) = - \frac{3}{4}

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

8 x = arcsin (- \frac{3}{4}) + 2 πn, 8 x = π + arcsin (\frac{3}{4}) + 2 πn

8 x = arcsin (- \frac{3}{4}) + 2 πn, 8 x = π + arcsin (\frac{3}{4}) + 2 πn

Resolver

8 x = arcsin (- \frac{3}{4}) + 2 πn : x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

8 x = arcsin (- \frac{3}{4}) + 2 πn

Simplificar

arcsin (- \frac{3}{4}) + 2 πn : - arcsin (\frac{3}{4}) + 2 πn

arcsin (- \frac{3}{4}) + 2 πn

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{4}) = - arcsin (\frac{3}{4})

= - arcsin (\frac{3}{4}) + 2 πn

8 x = - arcsin (\frac{3}{4}) + 2 πn

Dividir ambos lados entre

8

8 x = - arcsin (\frac{3}{4}) + 2 πn

Dividir ambos lados entre

8

\frac{8 x}{8} = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{2 πn}{8}

Simplificar

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

Resolver

8 x = π + arcsin (\frac{3}{4}) + 2 πn : x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

8 x = π + arcsin (\frac{3}{4}) + 2 πn

Dividir ambos lados entre

8

8 x = π + arcsin (\frac{3}{4}) + 2 πn

Dividir ambos lados entre

8

\frac{8 x}{8} = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{2 πn}{8}

Simplificar

x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

Mostrar soluciones en forma decimal

x = - \frac{0.84806 \dots}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{0.84806 \dots}{8} + \frac{πn}{4}

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tan (\frac{θ}{2}) - sin (θ) = 0