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0=3sin(x-1/2 pi)+2

Solución

0 = 3 sin (x - \frac{1}{2} π) + 2

Solución

x = - 0.72972 \dots + 2 πn + \frac{π}{2}, x = π + 0.72972 \dots + 2 πn + \frac{π}{2}

+1

Grados

x = 48.18968 \dots^{\circ} + 36 0^{\circ} n, x = 311.81031 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

0 = 3 sin (x - \frac{1}{2} π) + 2

Intercambiar lados

3 sin (x - \frac{1}{2} π) + 2 = 0

Mover

2

al lado derecho

3 sin (x - \frac{1}{2} π) + 2 = 0

Restar

2

de ambos lados

3 sin (x - \frac{1}{2} π) + 2 - 2 = 0 - 2

Simplificar

3 sin (x - \frac{1}{2} π) = - 2

3 sin (x - \frac{1}{2} π) = - 2

Dividir ambos lados entre

3

3 sin (x - \frac{1}{2} π) = - 2

Dividir ambos lados entre

3

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

Simplificar

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

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

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

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

Resolver

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

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

Simplificar

x - \frac{1}{2} π : x - \frac{π}{2}

x - \frac{1}{2} π

\frac{1}{2} π = \frac{π}{2}

\frac{1}{2} π

Multiplicar fracciones:

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

= \frac{1 π}{2}

Multiplicar:

1 π = π

= \frac{π}{2}

= x - \frac{π}{2}

Simplificar

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

arcsin (- \frac{2}{3}) + 2 πn

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{3}) = - arcsin (\frac{2}{3})

= - arcsin (\frac{2}{3}) + 2 πn

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

Mover

\frac{π}{2}

al lado derecho

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

Sumar

\frac{π}{2}

a ambos lados

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

Simplificar

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

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

Resolver

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

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

\frac{1}{2} π = \frac{π}{2}

\frac{1}{2} π

Multiplicar fracciones:

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

= \frac{1 π}{2}

Multiplicar:

1 π = π

= \frac{π}{2}

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

Mover

\frac{π}{2}

al lado derecho

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

Sumar

\frac{π}{2}

a ambos lados

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

Simplificar

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

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

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

Mostrar soluciones en forma decimal

x = - 0.72972 \dots + 2 πn + \frac{π}{2}, x = π + 0.72972 \dots + 2 πn + \frac{π}{2}

Ejemplos populares

2sin^2(x)=3sin(x)

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

5 + 2 sin (x) - 7 = 0

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0.5 = 1 - sin (θ)

solvefor θ,r=6sin(2θ)resolver para

θ, r = 6 sin (2 θ)