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Popular >

5sin(2x-pi/2)=0.5

Solución

5 sin (2 x - \frac{π}{2}) = 0.5

Solución

x = πn + \frac{π}{4} + \frac{0.10016 \dots}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{0.10016 \dots}{2}

Grados

x = 47.86958 \dots^{\circ} + 18 0^{\circ} n, x = 132.13041 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

5 sin (2 x - \frac{π}{2}) = 0.5

Dividir ambos lados entre

5

5 sin (2 x - \frac{π}{2}) = 0.5

Dividir ambos lados entre

5

\frac{5 sin ( 2 x - \frac{π}{2} )}{5} = \frac{0.5}{5}

Simplificar

sin (2 x - \frac{π}{2}) = 0.1

sin (2 x - \frac{π}{2}) = 0.1

Aplicar propiedades trigonométricas inversas

sin (2 x - \frac{π}{2}) = 0.1

Soluciones generales para

sin (2 x - \frac{π}{2}) = 0.1

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

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn, 2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn, 2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

Resolver

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn : x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn

Mover

\frac{π}{2}

al lado derecho

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn

Sumar

\frac{π}{2}

a ambos lados

2 x - \frac{π}{2} + \frac{π}{2} = arcsin (0.1) + 2 πn + \frac{π}{2}

Simplificar

2 x = arcsin (0.1) + 2 πn + \frac{π}{2}

2 x = arcsin (0.1) + 2 πn + \frac{π}{2}

Dividir ambos lados entre

2

2 x = arcsin (0.1) + 2 πn + \frac{π}{2}

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

Simplificar

\frac{2 x}{2} = \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2} : πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

\frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

Agrupar términos semejantes

= \frac{2 πn}{2} + \frac{\frac{π}{2}}{2} + \frac{arcsin ( 0.1 )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{π}{4}

= πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

Resolver

2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn : x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

Mover

\frac{π}{2}

al lado derecho

2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

Sumar

\frac{π}{2}

a ambos lados

2 x - \frac{π}{2} + \frac{π}{2} = π - arcsin (0.1) + 2 πn + \frac{π}{2}

Simplificar

2 x = π - arcsin (0.1) + 2 πn + \frac{π}{2}

2 x = π - arcsin (0.1) + 2 πn + \frac{π}{2}

Dividir ambos lados entre

2

2 x = π - arcsin (0.1) + 2 πn + \frac{π}{2}

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

Simplificar

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{π}{2} - \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2} : πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

\frac{π}{2} - \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

Agrupar términos semejantes

= \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2} - \frac{arcsin ( 0.1 )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{π}{4}

= \frac{π}{2} + πn + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

Agrupar términos semejantes

= πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

Mostrar soluciones en forma decimal

x = πn + \frac{π}{4} + \frac{0.10016 \dots}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{0.10016 \dots}{2}

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