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5sin(2x)=2tan(30)

Solución

5 sin (2 x) = 2 tan (3 0^{\circ})

Solución

x = \frac{0.23304 \dots}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{0.23304 \dots}{2} + 18 0^{\circ} n

radianes

x = \frac{0.23304 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.23304 \dots}{2} + πn

Pasos de solución

5 sin (2 x) = 2 tan (3 0^{\circ})

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

Utilizar la siguiente identidad trivial:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

tabla de valores periódicos con

18 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{3}{3}

5 sin (2 x) = 2 \cdot \frac{3}{3}

Dividir ambos lados entre

5

5 sin (2 x) = 2 \cdot \frac{3}{3}

Dividir ambos lados entre

5

\frac{5 sin ( 2 x )}{5} = \frac{2 \cdot \frac{3}{3}}{5}

Simplificar

\frac{5 sin ( 2 x )}{5} = \frac{2 \cdot \frac{3}{3}}{5}

Simplificar

\frac{5 sin ( 2 x )}{5} : sin (2 x)

\frac{5 sin ( 2 x )}{5}

Dividir:

\frac{5}{5} = 1

= sin (2 x)

Simplificar

\frac{2 \cdot \frac{3}{3}}{5} : \frac{2 3}{15}

\frac{2 \cdot \frac{3}{3}}{5}

Multiplicar

2 \cdot \frac{3}{3} : \frac{2}{3}

2 \cdot \frac{3}{3}

Multiplicar fracciones:

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

= \frac{3 \cdot 2}{3}

Aplicar las leyes de los exponentes:

3 = 3^{\frac{1}{2}}

= \frac{2 \cdot 3 ^{\frac{1}{2}}}{3}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{2}{3 ^{1 - \frac{1}{2}}}

Restar:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2}{3 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

3^{\frac{1}{2}} = 3

= \frac{2}{3}

= \frac{\frac{2}{3}}{5}

Aplicar las propiedades de las fracciones:

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

= \frac{2}{3 \cdot 5}

Racionalizar

\frac{2}{5 3} : \frac{2 3}{15}

\frac{2}{5 3}

Multiplicar por el conjugado

\frac{3}{3}

= \frac{2 3}{3 \cdot 5 3}

3 \cdot 53 = 15

3 \cdot 53

Aplicar las leyes de los exponentes:

a a = a

33 = 3

= 5 \cdot 3

Multiplicar los numeros:

5 \cdot 3 = 15

= 15

= \frac{2 3}{15}

= \frac{2 3}{15}

sin (2 x) = \frac{2 3}{15}

sin (2 x) = \frac{2 3}{15}

sin (2 x) = \frac{2 3}{15}

Aplicar propiedades trigonométricas inversas

sin (2 x) = \frac{2 3}{15}

Soluciones generales para

sin (2 x) = \frac{2 3}{15}

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

2 x = arcsin (\frac{2 3}{15}) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (\frac{2 3}{15}) + 36 0^{\circ} n

2 x = arcsin (\frac{2 3}{15}) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (\frac{2 3}{15}) + 36 0^{\circ} n

Resolver

2 x = arcsin (\frac{2 3}{15}) + 36 0^{\circ} n : x = \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

2 x = arcsin (\frac{2 3}{15}) + 36 0^{\circ} n

Simplificar

arcsin (\frac{2 3}{15}) + 36 0^{\circ} n : arcsin (\frac{2}{5 3}) + 36 0^{\circ} n

arcsin (\frac{2 3}{15}) + 36 0^{\circ} n

\frac{2 3}{15} = \frac{2}{5 3}

\frac{2 3}{15}

Factorizar

15 : 3 \cdot 5

Factorizar

15 = 3 \cdot 5

= \frac{2 3}{3 \cdot 5}

Cancelar

\frac{2 3}{3 \cdot 5} : \frac{2}{3 \cdot 5}

\frac{2 3}{3 \cdot 5}

Aplicar las leyes de los exponentes:

3 = 3^{\frac{1}{2}}

= \frac{2 \cdot 3 ^{\frac{1}{2}}}{3 \cdot 5}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{2}{5 \cdot 3 ^{- \frac{1}{2} + 1}}

Restar:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2}{5 \cdot 3 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

3^{\frac{1}{2}} = 3

= \frac{2}{5 3}

= \frac{2}{3 \cdot 5}

= arcsin (\frac{2}{5 3}) + 36 0^{\circ} n

2 x = arcsin (\frac{2}{5 3}) + 36 0^{\circ} n

Dividir ambos lados entre

2

2 x = arcsin (\frac{2}{5 3}) + 36 0^{\circ} n

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arcsin ( \frac{2}{5 3} )}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

\frac{2 x}{2} = \frac{arcsin ( \frac{2}{5 3} )}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{arcsin ( \frac{2}{5 3} )}{2} + \frac{36 0 ^{\circ} n}{2} : \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

\frac{arcsin ( \frac{2}{5 3} )}{2} + \frac{36 0 ^{\circ} n}{2}

arcsin (\frac{2}{5 3}) = arcsin (\frac{2 3}{15})

arcsin (\frac{2}{5 3})

= arcsin (\frac{2 3}{15})

= \frac{arcsin ( \frac{2 3}{15} )}{2} + \frac{36 0 ^{\circ} n}{2}

Dividir:

\frac{2}{2} = 1

= \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

\frac{2 3}{15} = \frac{2}{5 3}

\frac{2 3}{15}

Factorizar

15 : 3 \cdot 5

Factorizar

15 = 3 \cdot 5

= \frac{2 3}{3 \cdot 5}

Cancelar

\frac{2 3}{3 \cdot 5} : \frac{2}{3 \cdot 5}

\frac{2 3}{3 \cdot 5}

Aplicar las leyes de los exponentes:

3 = 3^{\frac{1}{2}}

= \frac{2 \cdot 3 ^{\frac{1}{2}}}{3 \cdot 5}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{2}{5 \cdot 3 ^{- \frac{1}{2} + 1}}

Restar:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2}{5 \cdot 3 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

3^{\frac{1}{2}} = 3

= \frac{2}{5 3}

= \frac{2}{3 \cdot 5}

= \frac{arcsin ( \frac{2}{5 3} )}{2} + 18 0^{\circ} n

arcsin (\frac{2}{3 \cdot 5}) = arcsin (\frac{2 3}{15})

arcsin (\frac{2}{3 \cdot 5})

= arcsin (\frac{2 3}{15})

= \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

Resolver

2 x = 18 0^{\circ} - arcsin (\frac{2 3}{15}) + 36 0^{\circ} n : x = 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

2 x = 18 0^{\circ} - arcsin (\frac{2 3}{15}) + 36 0^{\circ} n

Simplificar

18 0^{\circ} - arcsin (\frac{2 3}{15}) + 36 0^{\circ} n : 18 0^{\circ} - arcsin (\frac{2}{5 3}) + 36 0^{\circ} n

18 0^{\circ} - arcsin (\frac{2 3}{15}) + 36 0^{\circ} n

\frac{2 3}{15} = \frac{2}{5 3}

\frac{2 3}{15}

Factorizar

15 : 3 \cdot 5

Factorizar

15 = 3 \cdot 5

= \frac{2 3}{3 \cdot 5}

Cancelar

\frac{2 3}{3 \cdot 5} : \frac{2}{3 \cdot 5}

\frac{2 3}{3 \cdot 5}

Aplicar las leyes de los exponentes:

3 = 3^{\frac{1}{2}}

= \frac{2 \cdot 3 ^{\frac{1}{2}}}{3 \cdot 5}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{2}{5 \cdot 3 ^{- \frac{1}{2} + 1}}

Restar:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2}{5 \cdot 3 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

3^{\frac{1}{2}} = 3

= \frac{2}{5 3}

= \frac{2}{3 \cdot 5}

= 18 0^{\circ} - arcsin (\frac{2}{5 3}) + 36 0^{\circ} n

2 x = 18 0^{\circ} - arcsin (\frac{2}{5 3}) + 36 0^{\circ} n

Dividir ambos lados entre

2

2 x = 18 0^{\circ} - arcsin (\frac{2}{5 3}) + 36 0^{\circ} n

Dividir ambos lados entre

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arcsin ( \frac{2}{5 3} )}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

\frac{2 x}{2} = 9 0^{\circ} - \frac{arcsin ( \frac{2}{5 3} )}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

9 0^{\circ} - \frac{arcsin ( \frac{2}{5 3} )}{2} + \frac{36 0 ^{\circ} n}{2} : 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

9 0^{\circ} - \frac{arcsin ( \frac{2}{5 3} )}{2} + \frac{36 0 ^{\circ} n}{2}

arcsin (\frac{2}{5 3}) = arcsin (\frac{2 3}{15})

arcsin (\frac{2}{5 3})

= arcsin (\frac{2 3}{15})

= 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + \frac{36 0 ^{\circ} n}{2}

Dividir:

\frac{2}{2} = 1

= 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

\frac{2 3}{15} = \frac{2}{5 3}

\frac{2 3}{15}

Factorizar

15 : 3 \cdot 5

Factorizar

15 = 3 \cdot 5

= \frac{2 3}{3 \cdot 5}

Cancelar

\frac{2 3}{3 \cdot 5} : \frac{2}{3 \cdot 5}

\frac{2 3}{3 \cdot 5}

Aplicar las leyes de los exponentes:

3 = 3^{\frac{1}{2}}

= \frac{2 \cdot 3 ^{\frac{1}{2}}}{3 \cdot 5}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{2}{5 \cdot 3 ^{- \frac{1}{2} + 1}}

Restar:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{2}{5 \cdot 3 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

3^{\frac{1}{2}} = 3

= \frac{2}{5 3}

= \frac{2}{3 \cdot 5}

= 9 0^{\circ} - \frac{arcsin ( \frac{2}{5 3} )}{2} + 18 0^{\circ} n

arcsin (\frac{2}{3 \cdot 5}) = arcsin (\frac{2 3}{15})

arcsin (\frac{2}{3 \cdot 5})

= arcsin (\frac{2 3}{15})

= 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

x = 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

x = 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

x = 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{arcsin ( \frac{2 3}{15} )}{2} + 18 0^{\circ} n

Mostrar soluciones en forma decimal

x = \frac{0.23304 \dots}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{0.23304 \dots}{2} + 18 0^{\circ} n

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