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3sin(2x)=2,0<= x<= pi

Solución

3 sin (2 x) = 2, 0 \leq x \leq π

Solución

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

+1

Grados

x = 20.90515 \dots^{\circ}, x = 69.09484 \dots^{\circ}

Pasos de solución

3 sin (2 x) = 2, 0 \leq x \leq π

Dividir ambos lados entre

3

3 sin (2 x) = 2

Dividir ambos lados entre

3

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

Soluciones para el rango

0 \leq x \leq π

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

Mostrar soluciones en forma decimal

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

Ejemplos populares

cos(θ)= 2/(2.24)

cos (θ) = \frac{2}{2.24}

cot (α) = \frac{2}{3}

- 900 cos (30 x) = 0

sin^2(x)=((9m-9))/7

sin^{2} (x) = \frac{( 9 m - 9 )}{7}

sin (x) = 0.55669