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Popular Trigonometría >

2=3sin(|5x|)+1

Solución

2 = 3 sin (∣ 5 x ∣) + 1

Solución

Sin soluci \overset{o}{ˊ} n para x \in R

Pasos de solución

2 = 3 sin (∣ 5 x ∣) + 1

Intercambiar lados

3 sin (∣ 5 x ∣) + 1 = 2

Desplace

1

a la derecha

3 sin (∣ 5 x ∣) + 1 = 2

Restar

1

de ambos lados

3 sin (∣ 5 x ∣) + 1 - 1 = 2 - 1

Simplificar

3 sin (∣ 5 x ∣) = 1

3 sin (∣ 5 x ∣) = 1

Dividir ambos lados entre

3

3 sin (∣ 5 x ∣) = 1

Dividir ambos lados entre

3

\frac{3 sin ( ∣ 5 x ∣ )}{3} = \frac{1}{3}

Simplificar

sin (∣ 5 x ∣) = \frac{1}{3}

sin (∣ 5 x ∣) = \frac{1}{3}

Aplicar propiedades trigonométricas inversas

sin (∣ 5 x ∣) = \frac{1}{3}

Soluciones generales para

sin (∣ 5 x ∣) = \frac{1}{3}

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

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn, ∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn, ∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

Resolver

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn :

Sin solución

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn

Aplicar las propiedades de los valores absolutos: Pi

∣ u ∣ = a, a > 0

entonces

u = a

u = - a

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) : x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = - (arcsin (\frac{1}{3}) + 2 πn)

Dividir ambos lados entre

5

5 x = - (arcsin (\frac{1}{3}) + 2 πn)

Dividir ambos lados entre

5

\frac{5 x}{5} = \frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Simplificar

\frac{5 x}{5} = \frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Simplificar

\frac{5 x}{5} : x

\frac{5 x}{5}

Dividir:

\frac{5}{5} = 1

= x

Simplificar

\frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5} : - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Aplicar las propiedades de las fracciones:

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

= - \frac{( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Quitar los parentesis:

(a) = a

= - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = arcsin (\frac{1}{3}) + 2 πn : x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = arcsin (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

5

5 x = arcsin (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

5

\frac{5 x}{5} = \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Simplificar

\frac{5 x}{5} = \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Simplificar

\frac{5 x}{5} : x

\frac{5 x}{5}

Dividir:

\frac{5}{5} = 1

= x

Simplificar

\frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5} : \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Aplicar la regla

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

= \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

Combinar soluciones:

Sin soluci \overset{o}{ˊ} n or Sin soluci \overset{o}{ˊ} n

Sin soluci \overset{o}{ˊ} n or Sin soluci \overset{o}{ˊ} n

Sin soluci \overset{o}{ˊ} n para x \in R

Resolver

∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn :

Sin solución

∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

Aplicar las propiedades de los valores absolutos: Pi

∣ u ∣ = a, a > 0

entonces

u = a

u = - a

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) : x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

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

Dividir ambos lados entre

5

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

Dividir ambos lados entre

5

\frac{5 x}{5} = \frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Simplificar

\frac{5 x}{5} = \frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Simplificar

\frac{5 x}{5} : x

\frac{5 x}{5}

Dividir:

\frac{5}{5} = 1

= x

Simplificar

\frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5} : - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Aplicar las propiedades de las fracciones:

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

= - \frac{( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

Quitar los parentesis:

(a) = a

= - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = π - arcsin (\frac{1}{3}) + 2 πn : x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = π - arcsin (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

5

5 x = π - arcsin (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

5

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Simplificar

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Simplificar

\frac{5 x}{5} : x

\frac{5 x}{5}

Dividir:

\frac{5}{5} = 1

= x

Simplificar

\frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5} : \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

Aplicar la regla

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

= \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

Combinar soluciones:

Sin soluci \overset{o}{ˊ} n or Sin soluci \overset{o}{ˊ} n

Sin soluci \overset{o}{ˊ} n or Sin soluci \overset{o}{ˊ} n

Sin soluci \overset{o}{ˊ} n para x \in R

x = Sin soluci \overset{o}{ˊ} n, x = Sin soluci \overset{o}{ˊ} n

Siendo que la ecuación esta indefinida para:

Sin solución

Sin soluci \overset{o}{ˊ} n para x \in R

Gráfica

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cos(θ)=(-sqrt(3))/2

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