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solvefor x,h=4-2sin(3x+pi/3)

Solución

resolver para

x, h = 4 - 2 sin (3 x + \frac{π}{3})

Solución

x = \frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{π}{9}, x = \frac{π}{3} - \frac{π}{9} + \frac{2 πn}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

Pasos de solución

h = 4 - 2 sin (3 x + \frac{π}{3})

Intercambiar lados

4 - 2 sin (3 x + \frac{π}{3}) = h

Mover

4

al lado derecho

4 - 2 sin (3 x + \frac{π}{3}) = h

Restar

4

de ambos lados

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

Simplificar

- 2 sin (3 x + \frac{π}{3}) = h - 4

- 2 sin (3 x + \frac{π}{3}) = h - 4

Dividir ambos lados entre

- 2

- 2 sin (3 x + \frac{π}{3}) = h - 4

Dividir ambos lados entre

- 2

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

Simplificar

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

Simplificar

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

\frac{- 2 sin ( 3 x + \frac{π}{3} )}{- 2}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 sin ( 3 x + \frac{π}{3} )}{2}

Dividir:

\frac{2}{2} = 1

= sin (3 x + \frac{π}{3})

Simplificar

\frac{h}{- 2} - \frac{4}{- 2} : - \frac{h - 4}{2}

\frac{h}{- 2} - \frac{4}{- 2}

Aplicar la regla

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

= \frac{h - 4}{- 2}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{h - 4}{2}

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

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

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

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

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

Resolver

3 x + \frac{π}{3} = arcsin (- \frac{h - 4}{2}) + 2 πn : x = \frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{π}{9}

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

Mover

\frac{π}{3}

al lado derecho

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

Restar

\frac{π}{3}

de ambos lados

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

Simplificar

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

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

Dividir ambos lados entre

3

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

Dividir ambos lados entre

3

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

Simplificar

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

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{\frac{π}{3}}{3} : \frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{π}{9}

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

\frac{\frac{π}{3}}{3} = \frac{π}{9}

\frac{\frac{π}{3}}{3}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{3 \cdot 3}

Multiplicar los numeros:

3 \cdot 3 = 9

= \frac{π}{9}

= \frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{π}{9}

x = \frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{π}{9}

x = \frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{π}{9}

x = \frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{π}{9}

Resolver

3 x + \frac{π}{3} = π + arcsin (\frac{h - 4}{2}) + 2 πn : x = \frac{π}{3} - \frac{π}{9} + \frac{2 πn}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

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

Mover

\frac{π}{3}

al lado derecho

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

Restar

\frac{π}{3}

de ambos lados

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

Simplificar

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

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

Dividir ambos lados entre

3

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

Dividir ambos lados entre

3

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

Simplificar

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

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{π}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{\frac{π}{3}}{3} : \frac{π}{3} - \frac{π}{9} + \frac{2 πn}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

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

Agrupar términos semejantes

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

\frac{\frac{π}{3}}{3} = \frac{π}{9}

\frac{\frac{π}{3}}{3}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{3 \cdot 3}

Multiplicar los numeros:

3 \cdot 3 = 9

= \frac{π}{9}

= \frac{π}{3} + \frac{2 πn}{3} - \frac{π}{9} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

Agrupar términos semejantes

= \frac{π}{3} - \frac{π}{9} + \frac{2 πn}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

x = \frac{π}{3} - \frac{π}{9} + \frac{2 πn}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

x = \frac{π}{3} - \frac{π}{9} + \frac{2 πn}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

x = \frac{π}{3} - \frac{π}{9} + \frac{2 πn}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

x = \frac{arcsin ( - \frac{h - 4}{2} )}{3} + \frac{2 πn}{3} - \frac{π}{9}, x = \frac{π}{3} - \frac{π}{9} + \frac{2 πn}{3} + \frac{arcsin ( \frac{h - 4}{2} )}{3}

Ejemplos populares

sin^2(x)=2cos(x)+1

sin^{2} (x) = 2 cos (x) + 1

sin^2(x)+tan^2(x)=0

sin^{2} (x) + tan^{2} (x) = 0

tan(x)= 9/12

tan (x) = \frac{9}{12}

cos(x)= 24/25

cos (x) = \frac{24}{25}

2(tan(θ)+3)=5+tan(θ),0<= θ<2pi

2 (tan (θ) + 3) = 5 + tan (θ), 0 \leq θ < 2 π