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Popular >

2sin(2x+15)= 1/2

Solución

2 sin (2 x + 15) = \frac{1}{2}

Solución

x = πn - \frac{15}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{0.25268 \dots}{2}

Grados

x = - 422.47959 \dots^{\circ} + 18 0^{\circ} n, x = - 346.95710 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

2 sin (2 x + 15) = \frac{1}{2}

Dividir ambos lados entre

2

2 sin (2 x + 15) = \frac{1}{2}

Dividir ambos lados entre

2

\frac{2 sin ( 2 x + 15 )}{2} = \frac{\frac{1}{2}}{2}

Simplificar

\frac{2 sin ( 2 x + 15 )}{2} = \frac{\frac{1}{2}}{2}

Simplificar

\frac{2 sin ( 2 x + 15 )}{2} : sin (2 x + 15)

\frac{2 sin ( 2 x + 15 )}{2}

Dividir:

\frac{2}{2} = 1

= sin (2 x + 15)

Simplificar

\frac{\frac{1}{2}}{2} : \frac{1}{4}

\frac{\frac{1}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{1}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

Aplicar propiedades trigonométricas inversas

sin (2 x + 15) = \frac{1}{4}

Soluciones generales para

sin (2 x + 15) = \frac{1}{4}

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

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn, 2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn, 2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

Resolver

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn : x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn

Mover

15

al lado derecho

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn

Restar

15

de ambos lados

2 x + 15 - 15 = arcsin (\frac{1}{4}) + 2 πn - 15

Simplificar

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

Dividir ambos lados entre

2

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplificar

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2} : πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

\frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Agrupar términos semejantes

= - \frac{15}{2} + \frac{2 πn}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

Dividir:

\frac{2}{2} = 1

= - \frac{15}{2} + πn + \frac{arcsin ( \frac{1}{4} )}{2}

Agrupar términos semejantes

= πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

Resolver

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn : x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

Mover

15

al lado derecho

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

Restar

15

de ambos lados

2 x + 15 - 15 = π - arcsin (\frac{1}{4}) + 2 πn - 15

Simplificar

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

Dividir ambos lados entre

2

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplificar

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2} : πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

\frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Agrupar términos semejantes

= \frac{π}{2} - \frac{15}{2} + \frac{2 πn}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

Dividir:

\frac{2}{2} = 1

= \frac{π}{2} - \frac{15}{2} + πn - \frac{arcsin ( \frac{1}{4} )}{2}

Agrupar términos semejantes

= πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

Mostrar soluciones en forma decimal

x = πn - \frac{15}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{0.25268 \dots}{2}

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