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Popular >

5sin(2θ)=-1/5

Solución

5 sin (2 θ) = - \frac{1}{5}

Solución

θ = - \frac{0.04001 \dots}{2} + πn, θ = \frac{π}{2} + \frac{0.04001 \dots}{2} + πn

+1

Grados

θ = - 1.14622 \dots^{\circ} + 18 0^{\circ} n, θ = 91.14622 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

5 sin (2 θ) = - \frac{1}{5}

Dividir ambos lados entre

5

5 sin (2 θ) = - \frac{1}{5}

Dividir ambos lados entre

5

\frac{5 sin ( 2 θ )}{5} = \frac{- \frac{1}{5}}{5}

Simplificar

\frac{5 sin ( 2 θ )}{5} = \frac{- \frac{1}{5}}{5}

Simplificar

\frac{5 sin ( 2 θ )}{5} : sin (2 θ)

\frac{5 sin ( 2 θ )}{5}

Dividir:

\frac{5}{5} = 1

= sin (2 θ)

Simplificar

\frac{- \frac{1}{5}}{5} : - \frac{1}{25}

\frac{- \frac{1}{5}}{5}

Aplicar las propiedades de las fracciones:

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

= - \frac{\frac{1}{5}}{5}

Aplicar las propiedades de las fracciones:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{\frac{1}{5}}{5} = \frac{1}{5 \cdot 5}

= - \frac{1}{5 \cdot 5}

Multiplicar los numeros:

5 \cdot 5 = 25

= - \frac{1}{25}

sin (2 θ) = - \frac{1}{25}

sin (2 θ) = - \frac{1}{25}

sin (2 θ) = - \frac{1}{25}

Aplicar propiedades trigonométricas inversas

sin (2 θ) = - \frac{1}{25}

Soluciones generales para

sin (2 θ) = - \frac{1}{25}

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

2 θ = arcsin (- \frac{1}{25}) + 2 πn, 2 θ = π + arcsin (\frac{1}{25}) + 2 πn

2 θ = arcsin (- \frac{1}{25}) + 2 πn, 2 θ = π + arcsin (\frac{1}{25}) + 2 πn

Resolver

2 θ = arcsin (- \frac{1}{25}) + 2 πn : θ = - \frac{arcsin ( \frac{1}{25} )}{2} + πn

2 θ = arcsin (- \frac{1}{25}) + 2 πn

Simplificar

arcsin (- \frac{1}{25}) + 2 πn : - arcsin (\frac{1}{25}) + 2 πn

arcsin (- \frac{1}{25}) + 2 πn

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{25}) = - arcsin (\frac{1}{25})

= - arcsin (\frac{1}{25}) + 2 πn

2 θ = - arcsin (\frac{1}{25}) + 2 πn

Dividir ambos lados entre

2

2 θ = - arcsin (\frac{1}{25}) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = - \frac{arcsin ( \frac{1}{25} )}{2} + \frac{2 πn}{2}

Simplificar

θ = - \frac{arcsin ( \frac{1}{25} )}{2} + πn

θ = - \frac{arcsin ( \frac{1}{25} )}{2} + πn

Resolver

2 θ = π + arcsin (\frac{1}{25}) + 2 πn : θ = \frac{π}{2} + \frac{arcsin ( \frac{1}{25} )}{2} + πn

2 θ = π + arcsin (\frac{1}{25}) + 2 πn

Dividir ambos lados entre

2

2 θ = π + arcsin (\frac{1}{25}) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{π}{2} + \frac{arcsin ( \frac{1}{25} )}{2} + \frac{2 πn}{2}

Simplificar

θ = \frac{π}{2} + \frac{arcsin ( \frac{1}{25} )}{2} + πn

θ = \frac{π}{2} + \frac{arcsin ( \frac{1}{25} )}{2} + πn

θ = - \frac{arcsin ( \frac{1}{25} )}{2} + πn, θ = \frac{π}{2} + \frac{arcsin ( \frac{1}{25} )}{2} + πn

Mostrar soluciones en forma decimal

θ = - \frac{0.04001 \dots}{2} + πn, θ = \frac{π}{2} + \frac{0.04001 \dots}{2} + πn

Ejemplos populares

sin(θ)= 8/17 ,cos(θ)= 15/17 ,tan(θ)

sin (θ) = \frac{8}{17}, cos (θ) = \frac{15}{17}, tan (θ)

1/(sin^2(x))= 1/(cos^2(x))

\frac{1}{sin ^{2} ( x )} = \frac{1}{cos ^{2} ( x )}

sin(θ)=-12/13 ,sec(θ)

sin (θ) = - \frac{12}{13}, sec (θ)

tan (x) = \frac{7}{10}

3 sec (x) = 3