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3sin(2x)+1=2

Solución

3 sin (2 x) + 1 = 2

Solución

x = \frac{0.33983 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.33983 \dots}{2} + πn

+1

Grados

x = 9.73561 \dots^{\circ} + 18 0^{\circ} n, x = 80.26438 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

3 sin (2 x) + 1 = 2

Mover

1

al lado derecho

3 sin (2 x) + 1 = 2

Restar

1

de ambos lados

3 sin (2 x) + 1 - 1 = 2 - 1

Simplificar

3 sin (2 x) = 1

3 sin (2 x) = 1

Dividir ambos lados entre

3

3 sin (2 x) = 1

Dividir ambos lados entre

3

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

Simplificar

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

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

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

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

Resolver

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

2 x = arcsin (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

2

2 x = arcsin (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

2

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

Simplificar

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

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

Resolver

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

2 x = π - arcsin (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

2

2 x = π - arcsin (\frac{1}{3}) + 2 πn

Dividir ambos lados entre

2

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

Simplificar

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

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

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

Mostrar soluciones en forma decimal

x = \frac{0.33983 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.33983 \dots}{2} + πn

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