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Popular Trigonometría >

3sin(2x)=-1.76

Solución

3 sin (2 x) = - 1.76

Solución

x = - \frac{0.62693 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.62693 \dots}{2} + πn

+1

Grados

x = - 17.96040 \dots^{\circ} + 18 0^{\circ} n, x = 107.96040 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

3 sin (2 x) = - 1.76

Dividir ambos lados entre

3

3 sin (2 x) = - 1.76

Dividir ambos lados entre

3

\frac{3 sin ( 2 x )}{3} = \frac{- 1.76}{3}

Simplificar

\frac{3 sin ( 2 x )}{3} = \frac{- 1.76}{3}

Simplificar

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

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

Dividir:

\frac{3}{3} = 1

= sin (2 x)

Simplificar

\frac{- 1.76}{3} : - 0.58666 \dots

\frac{- 1.76}{3}

Aplicar las propiedades de las fracciones:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1.76}{3}

Dividir:

\frac{1.76}{3} = 0.58666 \dots

= - 0.58666 \dots

sin (2 x) = - 0.58666 \dots

sin (2 x) = - 0.58666 \dots

sin (2 x) = - 0.58666 \dots

Aplicar propiedades trigonométricas inversas

sin (2 x) = - 0.58666 \dots

Soluciones generales para

sin (2 x) = - 0.58666 \dots

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

2 x = arcsin (- 0.58666 \dots) + 2 πn, 2 x = π + arcsin (0.58666 \dots) + 2 πn

2 x = arcsin (- 0.58666 \dots) + 2 πn, 2 x = π + arcsin (0.58666 \dots) + 2 πn

Resolver

2 x = arcsin (- 0.58666 \dots) + 2 πn : x = - \frac{arcsin ( 0.58666 \dots )}{2} + πn

2 x = arcsin (- 0.58666 \dots) + 2 πn

Simplificar

arcsin (- 0.58666 \dots) + 2 πn : - arcsin (0.58666 \dots) + 2 πn

arcsin (- 0.58666 \dots) + 2 πn

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- 0.58666 \dots) = - arcsin (0.58666 \dots)

= - arcsin (0.58666 \dots) + 2 πn

2 x = - arcsin (0.58666 \dots) + 2 πn

Dividir ambos lados entre

2

2 x = - arcsin (0.58666 \dots) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = - \frac{arcsin ( 0.58666 \dots )}{2} + \frac{2 πn}{2}

Simplificar

x = - \frac{arcsin ( 0.58666 \dots )}{2} + πn

x = - \frac{arcsin ( 0.58666 \dots )}{2} + πn

Resolver

2 x = π + arcsin (0.58666 \dots) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + πn

2 x = π + arcsin (0.58666 \dots) + 2 πn

Dividir ambos lados entre

2

2 x = π + arcsin (0.58666 \dots) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + πn

x = - \frac{arcsin ( 0.58666 \dots )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + πn

Mostrar soluciones en forma decimal

x = - \frac{0.62693 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.62693 \dots}{2} + πn

Gráfica

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