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Popular >

2sin(2x)=tan(2x)

Solución

2 sin (2 x) = tan (2 x)

Solución

x = πn, x = \frac{π}{2} + πn, x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Grados

x = 0^{\circ} + 18 0^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n, x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

Pasos de solución

2 sin (2 x) = tan (2 x)

Restar

tan (2 x)

de ambos lados

2 sin (2 x) - tan (2 x) = 0

Expresar con seno, coseno

- tan (2 x) + 2 sin (2 x)

Utilizar la identidad trigonométrica básica:

tan (x) = \frac{sin ( x )}{cos ( x )}

= - \frac{sin ( 2 x )}{cos ( 2 x )} + 2 sin (2 x)

Simplificar

- \frac{sin ( 2 x )}{cos ( 2 x )} + 2 sin (2 x) : \frac{- sin ( 2 x ) + 2 sin ( 2 x ) cos ( 2 x )}{cos ( 2 x )}

- \frac{sin ( 2 x )}{cos ( 2 x )} + 2 sin (2 x)

Convertir a fracción:

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

= - \frac{sin ( 2 x )}{cos ( 2 x )} + \frac{2 sin ( 2 x ) cos ( 2 x )}{cos ( 2 x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{- sin ( 2 x ) + 2 sin ( 2 x ) cos ( 2 x )}{cos ( 2 x )}

= \frac{- sin ( 2 x ) + 2 sin ( 2 x ) cos ( 2 x )}{cos ( 2 x )}

\frac{- sin ( 2 x ) + 2 cos ( 2 x ) sin ( 2 x )}{cos ( 2 x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- sin (2 x) + 2 cos (2 x) sin (2 x) = 0

Factorizar

- sin (2 x) + 2 cos (2 x) sin (2 x) : sin (2 x) (2 cos (2 x) - 1)

- sin (2 x) + 2 cos (2 x) sin (2 x)

Factorizar el termino común

sin (2 x)

= sin (2 x) (- 1 + 2 cos (2 x))

sin (2 x) (2 cos (2 x) - 1) = 0

Resolver cada parte por separado

sin (2 x) = 0 or 2 cos (2 x) - 1 = 0

sin (2 x) = 0 : x = πn, x = \frac{π}{2} + πn

sin (2 x) = 0

Soluciones generales para

sin (2 x) = 0

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 x = 0 + 2 πn, 2 x = π + 2 πn

2 x = 0 + 2 πn, 2 x = π + 2 πn

Resolver

2 x = 0 + 2 πn : x = πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

Dividir ambos lados entre

2

2 x = 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{2 πn}{2}

Simplificar

x = πn

x = πn

Resolver

2 x = π + 2 πn : x = \frac{π}{2} + πn

2 x = π + 2 πn

Dividir ambos lados entre

2

2 x = π + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

2 cos (2 x) - 1 = 0 : x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

2 cos (2 x) - 1 = 0

Mover

1

al lado derecho

2 cos (2 x) - 1 = 0

Sumar

1

a ambos lados

2 cos (2 x) - 1 + 1 = 0 + 1

Simplificar

2 cos (2 x) = 1

2 cos (2 x) = 1

Dividir ambos lados entre

2

2 cos (2 x) = 1

Dividir ambos lados entre

2

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

Simplificar

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

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

Soluciones generales para

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

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 x = \frac{π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

2 x = \frac{π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

Resolver

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

2 x = \frac{π}{3} + 2 πn

Dividir ambos lados entre

2

2 x = \frac{π}{3} + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} : \frac{π}{6} + πn

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{3 \cdot 2}

Multiplicar los numeros:

3 \cdot 2 = 6

= \frac{π}{6}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

Resolver

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

2 x = \frac{5 π}{3} + 2 πn

Dividir ambos lados entre

2

2 x = \frac{5 π}{3} + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{\frac{5 π}{3}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 x}{2} = \frac{\frac{5 π}{3}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{5 π}{3}}{2} + \frac{2 πn}{2} : \frac{5 π}{6} + πn

\frac{\frac{5 π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{5 π}{3}}{2} = \frac{5 π}{6}

\frac{\frac{5 π}{3}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{5 π}{3 \cdot 2}

Multiplicar los numeros:

3 \cdot 2 = 6

= \frac{5 π}{6}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Combinar toda las soluciones

x = πn, x = \frac{π}{2} + πn, x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Ejemplos populares

sin^2(3a)=0.56

sin^{2} (3 a) = 0.56

cos(x)=0.22

cos (x) = 0.22

3cos(b)-1=5cos(b)+1

3 cos (b) - 1 = 5 cos (b) + 1

sin(-x)=cos(x)

sin (- x) = cos (x)

tan(a)=(-4)/3

tan (a) = \frac{- 4}{3}