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Popular >

4sin(2x)tan(x)-tan(x)=0

Solución

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

Solución

x = πn, x = \frac{0.25268 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

+1

Grados

x = 0^{\circ} + 18 0^{\circ} n, x = 7.23875 \dots^{\circ} + 18 0^{\circ} n, x = 82.76124 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

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

Factorizar

4 sin (2 x) tan (x) - tan (x) : tan (x) (4 sin (2 x) - 1)

4 sin (2 x) tan (x) - tan (x)

Factorizar el termino común

tan (x)

= tan (x) (4 sin (2 x) - 1)

tan (x) (4 sin (2 x) - 1) = 0

Resolver cada parte por separado

tan (x) = 0 or 4 sin (2 x) - 1 = 0

tan (x) = 0 : x = πn

tan (x) = 0

Soluciones generales para

tan (x) = 0

tan (x)

tabla de valores periódicos con

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Resolver

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

4 sin (2 x) - 1 = 0 : x = \frac{arcsin ( \frac{1}{4} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

4 sin (2 x) - 1 = 0

Mover

1

al lado derecho

4 sin (2 x) - 1 = 0

Sumar

1

a ambos lados

4 sin (2 x) - 1 + 1 = 0 + 1

Simplificar

4 sin (2 x) = 1

4 sin (2 x) = 1

Dividir ambos lados entre

4

4 sin (2 x) = 1

Dividir ambos lados entre

4

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

Simplificar

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

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

2 x = arcsin (\frac{1}{4}) + 2 πn, 2 x = π - arcsin (\frac{1}{4}) + 2 πn

2 x = arcsin (\frac{1}{4}) + 2 πn, 2 x = π - arcsin (\frac{1}{4}) + 2 πn

Resolver

2 x = arcsin (\frac{1}{4}) + 2 πn : x = \frac{arcsin ( \frac{1}{4} )}{2} + πn

2 x = arcsin (\frac{1}{4}) + 2 πn

Dividir ambos lados entre

2

2 x = arcsin (\frac{1}{4}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{arcsin ( \frac{1}{4} )}{2} + πn

x = \frac{arcsin ( \frac{1}{4} )}{2} + πn

Resolver

2 x = π - arcsin (\frac{1}{4}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

2 x = π - arcsin (\frac{1}{4}) + 2 πn

Dividir ambos lados entre

2

2 x = π - arcsin (\frac{1}{4}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

x = \frac{arcsin ( \frac{1}{4} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

Combinar toda las soluciones

x = πn, x = \frac{arcsin ( \frac{1}{4} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

Mostrar soluciones en forma decimal

x = πn, x = \frac{0.25268 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

Ejemplos populares

3sin(x)=sqrt(3)*sin(x)+3cos(x)+3sin(x)

3 sin (x) = 3 \cdot sin (x) + 3 cos (x) + 3 sin (x)

csc(θ)+1=0,(0,2pi)

csc (θ) + 1 = 0, (0, 2 π)

solvefor x,y^2=-2tan(2x)resolver para

x, y^{2} = - 2 tan (2 x)

2cos^2(a)-3cos(a)+1=0

2 cos^{2} (a) - 3 cos (a) + 1 = 0

sin(x)*cos(2x)=0.5-sin(2x)*cos(x)

sin (x) \cdot cos (2 x) = 0.5 - sin (2 x) \cdot cos (x)