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Popular >

sin(2θ)=-24/25 ,sin(θ)= 3/5

Solución

sin (2 θ) = - \frac{24}{25}, sin (θ) = \frac{3}{5}

Sin soluci \overset{o}{ˊ} n para θ \in R

Pasos de solución

sin (2 θ) = - \frac{24}{25}, sin (θ) = \frac{3}{5}

Aplicar propiedades trigonométricas inversas

sin (2 θ) = - \frac{24}{25}

Soluciones generales para

sin (2 θ) = - \frac{24}{25}

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

2 θ = arcsin (- \frac{24}{25}) + 2 πn, 2 θ = π + arcsin (\frac{24}{25}) + 2 πn

2 θ = arcsin (- \frac{24}{25}) + 2 πn, 2 θ = π + arcsin (\frac{24}{25}) + 2 πn

Resolver

2 θ = arcsin (- \frac{24}{25}) + 2 πn : θ = - \frac{arcsin ( \frac{24}{25} )}{2} + πn

2 θ = arcsin (- \frac{24}{25}) + 2 πn

Simplificar

arcsin (- \frac{24}{25}) + 2 πn : - arcsin (\frac{24}{25}) + 2 πn

arcsin (- \frac{24}{25}) + 2 πn

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{24}{25}) = - arcsin (\frac{24}{25})

= - arcsin (\frac{24}{25}) + 2 πn

2 θ = - arcsin (\frac{24}{25}) + 2 πn

Dividir ambos lados entre

2

2 θ = - arcsin (\frac{24}{25}) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = - \frac{arcsin ( \frac{24}{25} )}{2} + \frac{2 πn}{2}

Simplificar

θ = - \frac{arcsin ( \frac{24}{25} )}{2} + πn

θ = - \frac{arcsin ( \frac{24}{25} )}{2} + πn

Resolver

2 θ = π + arcsin (\frac{24}{25}) + 2 πn : θ = \frac{π}{2} + \frac{arcsin ( \frac{24}{25} )}{2} + πn

2 θ = π + arcsin (\frac{24}{25}) + 2 πn

Dividir ambos lados entre

2

2 θ = π + arcsin (\frac{24}{25}) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{π}{2} + \frac{arcsin ( \frac{24}{25} )}{2} + \frac{2 πn}{2}

Simplificar

θ = \frac{π}{2} + \frac{arcsin ( \frac{24}{25} )}{2} + πn

θ = \frac{π}{2} + \frac{arcsin ( \frac{24}{25} )}{2} + πn

θ = - \frac{arcsin ( \frac{24}{25} )}{2} + πn, θ = \frac{π}{2} + \frac{arcsin ( \frac{24}{25} )}{2} + πn

Soluciones para el rango

sin (θ) = \frac{3}{5}

Sin soluci \overset{o}{ˊ} n para θ \in R

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sin (4 x) = \frac{1}{2}

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81 π = 10.5 - 9 cos (\frac{π}{30} t)

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