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Popular >

9sin(x-0.5pi)+8=0

Solución

9 sin (x - 0.5 π) + 8 = 0

Solución

x = - 1.09491 \dots + 2 πn + 0.5 π, x = 1.5 π + 2 πn + 1.09491 \dots

+1

Grados

x = 27.26604 \dots^{\circ} + 36 0^{\circ} n, x = 332.73395 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

9 sin (x - 0.5 π) + 8 = 0

Mover

8

al lado derecho

9 sin (x - 0.5 π) + 8 = 0

Restar

8

de ambos lados

9 sin (x - 0.5 π) + 8 - 8 = 0 - 8

Simplificar

9 sin (x - 0.5 π) = - 8

9 sin (x - 0.5 π) = - 8

Dividir ambos lados entre

9

9 sin (x - 0.5 π) = - 8

Dividir ambos lados entre

9

\frac{9 sin ( x - 0.5 π )}{9} = \frac{- 8}{9}

Simplificar

sin (x - 0.5 π) = - \frac{8}{9}

sin (x - 0.5 π) = - \frac{8}{9}

Aplicar propiedades trigonométricas inversas

sin (x - 0.5 π) = - \frac{8}{9}

Soluciones generales para

sin (x - 0.5 π) = - \frac{8}{9}

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

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn, x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn, x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

Resolver

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn : x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn

Simplificar

arcsin (- \frac{8}{9}) + 2 πn : - arcsin (\frac{8}{9}) + 2 πn

arcsin (- \frac{8}{9}) + 2 πn

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{8}{9}) = - arcsin (\frac{8}{9})

= - arcsin (\frac{8}{9}) + 2 πn

x - 0.5 π = - arcsin (\frac{8}{9}) + 2 πn

Mover

0.5 π

al lado derecho

x - 0.5 π = - arcsin (\frac{8}{9}) + 2 πn

Sumar

0.5 π

a ambos lados

x - 0.5 π + 0.5 π = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Simplificar

x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Resolver

x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn : x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

Mover

0.5 π

al lado derecho

x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

Sumar

0.5 π

a ambos lados

x - 0.5 π + 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Simplificar

x - 0.5 π + 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Simplificar

x - 0.5 π + 0.5 π : x

x - 0.5 π + 0.5 π

Sumar elementos similares:

- 0.5 π + 0.5 π = 0

= x

Simplificar

π + arcsin (\frac{8}{9}) + 2 πn + 0.5 π : 1.5 π + 2 πn + arcsin (\frac{8}{9})

π + arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Agrupar términos semejantes

= π + 0.5 π + 2 πn + arcsin (\frac{8}{9})

Sumar elementos similares:

π + 0.5 π = 1.5 π

= 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π, x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

Mostrar soluciones en forma decimal

x = - 1.09491 \dots + 2 πn + 0.5 π, x = 1.5 π + 2 πn + 1.09491 \dots

Ejemplos populares

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sin^2(x)+5cos^2(x)=3

sin^{2} (x) + 5 cos^{2} (x) = 3

sin(x-pi/2)+cos(x+pi/2)=0

sin (x - \frac{π}{2}) + cos (x + \frac{π}{2}) = 0