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Popular >

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

Solución

5 sin (\frac{2 x - π}{2}) = 0.5

Solución

x = \frac{π}{2} + 2 πn + 0.10016 \dots, x = \frac{3 π}{2} + 2 πn - 0.10016 \dots

Grados

x = 95.73917 \dots^{\circ} + 36 0^{\circ} n, x = 264.26082 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

5 sin (\frac{2 x - π}{2}) = 0.5

Dividir ambos lados entre

5

5 sin (\frac{2 x - π}{2}) = 0.5

Dividir ambos lados entre

5

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

Simplificar

sin (\frac{2 x - π}{2}) = 0.1

sin (\frac{2 x - π}{2}) = 0.1

Aplicar propiedades trigonométricas inversas

sin (\frac{2 x - π}{2}) = 0.1

Soluciones generales para

sin (\frac{2 x - π}{2}) = 0.1

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

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

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

Resolver

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

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

Multiplicar ambos lados por

2

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

Multiplicar ambos lados por

2

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

Simplificar

2 x - π = 2 arcsin (0.1) + 4 πn

2 x - π = 2 arcsin (0.1) + 4 πn

Mover

π

al lado derecho

2 x - π = 2 arcsin (0.1) + 4 πn

Sumar

π

a ambos lados

2 x - π + π = 2 arcsin (0.1) + 4 πn + π

Simplificar

2 x = 2 arcsin (0.1) + 4 πn + π

2 x = 2 arcsin (0.1) + 4 πn + π

Dividir ambos lados entre

2

2 x = 2 arcsin (0.1) + 4 πn + π

Dividir ambos lados entre

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

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

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

Agrupar términos semejantes

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

Dividir:

\frac{4}{2} = 2

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

Dividir:

\frac{2}{2} = 1

= \frac{π}{2} + 2 πn + arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1)

Resolver

\frac{2 x - π}{2} = π - arcsin (0.1) + 2 πn : x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

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

Multiplicar ambos lados por

2

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

Multiplicar ambos lados por

2

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

Simplificar

2 x - π = 2 π - 2 arcsin (0.1) + 4 πn

2 x - π = 2 π - 2 arcsin (0.1) + 4 πn

Mover

π

al lado derecho

2 x - π = 2 π - 2 arcsin (0.1) + 4 πn

Sumar

π

a ambos lados

2 x - π + π = 2 π - 2 arcsin (0.1) + 4 πn + π

Simplificar

2 x = 3 π + 4 πn - 2 arcsin (0.1)

2 x = 3 π + 4 πn - 2 arcsin (0.1)

Dividir ambos lados entre

2

2 x = 3 π + 4 πn - 2 arcsin (0.1)

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{3 π}{2} + \frac{4 πn}{2} - \frac{2 arcsin ( 0.1 )}{2}

Simplificar

\frac{2 x}{2} = \frac{3 π}{2} + \frac{4 πn}{2} - \frac{2 arcsin ( 0.1 )}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{3 π}{2} + \frac{4 πn}{2} - \frac{2 arcsin ( 0.1 )}{2} : \frac{3 π}{2} + 2 πn - arcsin (0.1)

\frac{3 π}{2} + \frac{4 πn}{2} - \frac{2 arcsin ( 0.1 )}{2}

Dividir:

\frac{4}{2} = 2

= \frac{3 π}{2} + 2 πn - \frac{2 arcsin ( 0.1 )}{2}

Dividir:

\frac{2}{2} = 1

= \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1), x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

Mostrar soluciones en forma decimal

x = \frac{π}{2} + 2 πn + 0.10016 \dots, x = \frac{3 π}{2} + 2 πn - 0.10016 \dots

Ejemplos populares

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16 sin^{2} (θ) = 12

tan(θ)=-(sqrt(57))/9

tan (θ) = - \frac{57}{9}

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sin^{2} (x) = \frac{2}{3}

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