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Popular Trigonometría >

h=3sin(2x-1)+4

Solución

h = 3 sin (2 x - 1) + 4

Solución

x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}, x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

Pasos de solución

h = 3 sin (2 x - 1) + 4

Intercambiar lados

3 sin (2 x - 1) + 4 = h

Desplace

4

a la derecha

3 sin (2 x - 1) + 4 = h

Restar

4

de ambos lados

3 sin (2 x - 1) + 4 - 4 = h - 4

Simplificar

3 sin (2 x - 1) = h - 4

3 sin (2 x - 1) = h - 4

Dividir ambos lados entre

3

3 sin (2 x - 1) = h - 4

Dividir ambos lados entre

3

\frac{3 sin ( 2 x - 1 )}{3} = \frac{h}{3} - \frac{4}{3}

Simplificar

\frac{3 sin ( 2 x - 1 )}{3} = \frac{h}{3} - \frac{4}{3}

Simplificar

\frac{3 sin ( 2 x - 1 )}{3} : sin (2 x - 1)

\frac{3 sin ( 2 x - 1 )}{3}

Dividir:

\frac{3}{3} = 1

= sin (2 x - 1)

Simplificar

\frac{h}{3} - \frac{4}{3} : \frac{h - 4}{3}

\frac{h}{3} - \frac{4}{3}

Aplicar la regla

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

= \frac{h - 4}{3}

sin (2 x - 1) = \frac{h - 4}{3}

sin (2 x - 1) = \frac{h - 4}{3}

sin (2 x - 1) = \frac{h - 4}{3}

Aplicar propiedades trigonométricas inversas

sin (2 x - 1) = \frac{h - 4}{3}

Soluciones generales para

sin (2 x - 1) = \frac{h - 4}{3}

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

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn, 2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn, 2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn

Resolver

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn : x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn

Desplace

1

a la derecha

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn

Sumar

1

a ambos lados

2 x - 1 + 1 = arcsin (\frac{h - 4}{3}) + 2 πn + 1

Simplificar

2 x = arcsin (\frac{h - 4}{3}) + 2 πn + 1

2 x = arcsin (\frac{h - 4}{3}) + 2 πn + 1

Dividir ambos lados entre

2

2 x = arcsin (\frac{h - 4}{3}) + 2 πn + 1

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arcsin ( \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2}

Simplificar

x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}

x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}

Resolver

2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn : x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn

Desplace

1

a la derecha

2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn

Sumar

1

a ambos lados

2 x - 1 + 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn + 1

Simplificar

2 x = π + arcsin (- \frac{h - 4}{3}) + 2 πn + 1

2 x = π + arcsin (- \frac{h - 4}{3}) + 2 πn + 1

Dividir ambos lados entre

2

2 x = π + arcsin (- \frac{h - 4}{3}) + 2 πn + 1

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2}

Simplificar

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{π}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2} : \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

\frac{π}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2}

Agrupar términos semejantes

= \frac{π}{2} + \frac{1}{2} + \frac{2 πn}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

Dividir:

\frac{2}{2} = 1

= \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}, x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

Gráfica

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