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arcsin(3x-pi)= 1/2

Solución

arcsin (3 x - π) = \frac{1}{2}

Solución

x = \frac{sin ( \frac{1}{2} ) + π}{3}

Pasos de solución

arcsin (3 x - π) = \frac{1}{2}

Aplicar propiedades trigonométricas inversas

arcsin (3 x - π) = \frac{1}{2}

arcsin (x) = a \Rightarrow x = sin (a)

3 x - π = sin (\frac{1}{2})

3 x - π = sin (\frac{1}{2})

Resolver

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

3 x - π = sin (\frac{1}{2})

Mover

π

al lado derecho

3 x - π = sin (\frac{1}{2})

Sumar

π

a ambos lados

3 x - π + π = sin (\frac{1}{2}) + π

Simplificar

3 x = sin (\frac{1}{2}) + π

3 x = sin (\frac{1}{2}) + π

Dividir ambos lados entre

3

3 x = sin (\frac{1}{2}) + π

Dividir ambos lados entre

3

\frac{3 x}{3} = \frac{sin ( \frac{1}{2} )}{3} + \frac{π}{3}

Simplificar

\frac{3 x}{3} = \frac{sin ( \frac{1}{2} )}{3} + \frac{π}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{sin ( \frac{1}{2} )}{3} + \frac{π}{3} : \frac{sin ( \frac{1}{2} ) + π}{3}

\frac{sin ( \frac{1}{2} )}{3} + \frac{π}{3}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{sin ( \frac{1}{2} ) + π}{3}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

x = \frac{sin ( \frac{1}{2} ) + π}{3}

Ejemplos populares

2cos^2(θ)+sin(θ)-1=0

2 cos^{2} (θ) + sin (θ) - 1 = 0

2sin(2x)sin(x)-3cos(x)=0

2 sin (2 x) sin (x) - 3 cos (x) = 0

sin(θ)=(sqrt(13))/7

sin (θ) = \frac{13}{7}

sin^2(θ)-cos^2(θ)=1

sin^{2} (θ) - cos^{2} (θ) = 1

2sin(3θ)=sqrt(2)

2 sin (3 θ) = 2