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Popular >

sin(2θ)=-1/8 ,270<θ<360

Solución

sin (2 θ) = - \frac{1}{8}, 27 0^{\circ} < θ < 36 0^{\circ}

Solución

θ = \frac{54 0 ^{\circ} + 0.12532 \dots}{2}, θ = \frac{- 0.12532 \dots + 72 0 ^{\circ}}{2}

+1

radianes

θ = \frac{3 π + 0.12532 \dots}{2}, θ = \frac{- 0.12532 \dots + 4 π}{2}

Pasos de solución

sin (2 θ) = - \frac{1}{8}, 27 0^{\circ} < θ < 36 0^{\circ}

Aplicar propiedades trigonométricas inversas

sin (2 θ) = - \frac{1}{8}

Soluciones generales para

sin (2 θ) = - \frac{1}{8}

sin (x) = - a \Rightarrow x = arcsin (- a) + 36 0^{\circ} n, x = 18 0^{\circ} + arcsin (a) + 36 0^{\circ} n

2 θ = arcsin (- \frac{1}{8}) + 36 0^{\circ} n, 2 θ = 18 0^{\circ} + arcsin (\frac{1}{8}) + 36 0^{\circ} n

2 θ = arcsin (- \frac{1}{8}) + 36 0^{\circ} n, 2 θ = 18 0^{\circ} + arcsin (\frac{1}{8}) + 36 0^{\circ} n

Resolver

2 θ = arcsin (- \frac{1}{8}) + 36 0^{\circ} n : θ = - \frac{arcsin ( \frac{1}{8} )}{2} + 18 0^{\circ} n

2 θ = arcsin (- \frac{1}{8}) + 36 0^{\circ} n

Simplificar

arcsin (- \frac{1}{8}) + 36 0^{\circ} n : - arcsin (\frac{1}{8}) + 36 0^{\circ} n

arcsin (- \frac{1}{8}) + 36 0^{\circ} n

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{8}) = - arcsin (\frac{1}{8})

= - arcsin (\frac{1}{8}) + 36 0^{\circ} n

2 θ = - arcsin (\frac{1}{8}) + 36 0^{\circ} n

Dividir ambos lados entre

2

2 θ = - arcsin (\frac{1}{8}) + 36 0^{\circ} n

Dividir ambos lados entre

2

\frac{2 θ}{2} = - \frac{arcsin ( \frac{1}{8} )}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

θ = - \frac{arcsin ( \frac{1}{8} )}{2} + 18 0^{\circ} n

θ = - \frac{arcsin ( \frac{1}{8} )}{2} + 18 0^{\circ} n

Resolver

2 θ = 18 0^{\circ} + arcsin (\frac{1}{8}) + 36 0^{\circ} n : θ = 9 0^{\circ} + \frac{arcsin ( \frac{1}{8} )}{2} + 18 0^{\circ} n

2 θ = 18 0^{\circ} + arcsin (\frac{1}{8}) + 36 0^{\circ} n

Dividir ambos lados entre

2

2 θ = 18 0^{\circ} + arcsin (\frac{1}{8}) + 36 0^{\circ} n

Dividir ambos lados entre

2

\frac{2 θ}{2} = 9 0^{\circ} + \frac{arcsin ( \frac{1}{8} )}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

θ = 9 0^{\circ} + \frac{arcsin ( \frac{1}{8} )}{2} + 18 0^{\circ} n

θ = 9 0^{\circ} + \frac{arcsin ( \frac{1}{8} )}{2} + 18 0^{\circ} n

θ = - \frac{arcsin ( \frac{1}{8} )}{2} + 18 0^{\circ} n, θ = 9 0^{\circ} + \frac{arcsin ( \frac{1}{8} )}{2} + 18 0^{\circ} n

Soluciones para el rango

27 0^{\circ} < θ < 36 0^{\circ}

θ = \frac{54 0 ^{\circ} + arcsin ( \frac{1}{8} )}{2}, θ = \frac{- arcsin ( \frac{1}{8} ) + 72 0 ^{\circ}}{2}

Mostrar soluciones en forma decimal

θ = \frac{54 0 ^{\circ} + 0.12532 \dots}{2}, θ = \frac{- 0.12532 \dots + 72 0 ^{\circ}}{2}

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