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Popular >

sin(2x+30)=0.8

Solución

sin (2 x + 30) = 0.8

Solución

x = - 15 + πn + \frac{0.92729 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.92729 \dots}{2} - 15

Grados

x = - 832.87164 \dots^{\circ} + 18 0^{\circ} n, x = - 796.00174 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

sin (2 x + 30) = 0.8

Aplicar propiedades trigonométricas inversas

sin (2 x + 30) = 0.8

Soluciones generales para

sin (2 x + 30) = 0.8

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

2 x + 30 = arcsin (0.8) + 2 πn, 2 x + 30 = π - arcsin (0.8) + 2 πn

2 x + 30 = arcsin (0.8) + 2 πn, 2 x + 30 = π - arcsin (0.8) + 2 πn

Resolver

2 x + 30 = arcsin (0.8) + 2 πn : x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

2 x + 30 = arcsin (0.8) + 2 πn

Mover

30

al lado derecho

2 x + 30 = arcsin (0.8) + 2 πn

Restar

30

de ambos lados

2 x + 30 - 30 = arcsin (0.8) + 2 πn - 30

Simplificar

2 x = arcsin (0.8) + 2 πn - 30

2 x = arcsin (0.8) + 2 πn - 30

Dividir ambos lados entre

2

2 x = arcsin (0.8) + 2 πn - 30

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Simplificar

\frac{2 x}{2} = \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2} : - 15 + πn + \frac{arcsin ( 0.8 )}{2}

\frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Agrupar términos semejantes

= - \frac{30}{2} + \frac{2 πn}{2} + \frac{arcsin ( 0.8 )}{2}

Dividir:

\frac{30}{2} = 15

= - 15 + \frac{2 πn}{2} + \frac{arcsin ( 0.8 )}{2}

Dividir:

\frac{2}{2} = 1

= - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

Resolver

2 x + 30 = π - arcsin (0.8) + 2 πn : x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

2 x + 30 = π - arcsin (0.8) + 2 πn

Mover

30

al lado derecho

2 x + 30 = π - arcsin (0.8) + 2 πn

Restar

30

de ambos lados

2 x + 30 - 30 = π - arcsin (0.8) + 2 πn - 30

Simplificar

2 x = π - arcsin (0.8) + 2 πn - 30

2 x = π - arcsin (0.8) + 2 πn - 30

Dividir ambos lados entre

2

2 x = π - arcsin (0.8) + 2 πn - 30

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Simplificar

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2} : πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

\frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Agrupar términos semejantes

= \frac{π}{2} - \frac{30}{2} + \frac{2 πn}{2} - \frac{arcsin ( 0.8 )}{2}

Dividir:

\frac{30}{2} = 15

= \frac{π}{2} - 15 + \frac{2 πn}{2} - \frac{arcsin ( 0.8 )}{2}

Dividir:

\frac{2}{2} = 1

= \frac{π}{2} - 15 + πn - \frac{arcsin ( 0.8 )}{2}

Agrupar términos semejantes

= πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}, x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

Mostrar soluciones en forma decimal

x = - 15 + πn + \frac{0.92729 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.92729 \dots}{2} - 15

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