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Popular >

sin(2x)-2/3 =0

Solución

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

Solución

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

+1

Grados

x = 20.90515 \dots^{\circ} + 18 0^{\circ} n, x = 69.09484 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

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

Mover

\frac{2}{3}

al lado derecho

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

Sumar

\frac{2}{3}

a ambos lados

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

Simplificar

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

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

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

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

Resolver

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

2 x = arcsin (\frac{2}{3}) + 2 πn

Dividir ambos lados entre

2

2 x = arcsin (\frac{2}{3}) + 2 πn

Dividir ambos lados entre

2

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

Simplificar

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

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

Resolver

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

2 x = π - arcsin (\frac{2}{3}) + 2 πn

Dividir ambos lados entre

2

2 x = π - arcsin (\frac{2}{3}) + 2 πn

Dividir ambos lados entre

2

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

Simplificar

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

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

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

Mostrar soluciones en forma decimal

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

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