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Popular >

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

Solución

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

Solución

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

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Restar

sin (2 x)

de ambos lados

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

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad trigonométrica del ángulo doble:

sin (2 x) = 2 sin (x) cos (x)

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

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

Factorizar

cos (x) tan (x) - 2 cos (x) sin (x) : cos (x) (tan (x) - 2 sin (x))

cos (x) tan (x) - 2 cos (x) sin (x)

Factorizar el termino común

cos (x)

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

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

Resolver cada parte por separado

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

Soluciones generales para

cos (x) = 0

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}

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

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

tan (x) - 2 sin (x) = 0 : x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

Expresar con seno, coseno

tan (x) - 2 sin (x)

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

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

Convertir a fracción:

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

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

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

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

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

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

Factorizar

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

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

Factorizar el termino común

- sin (x)

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

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

Resolver cada parte por separado

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

Soluciones generales para

sin (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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 cos (x) - 1 = 0

Mover

1

al lado derecho

2 cos (x) - 1 = 0

Sumar

1

a ambos lados

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

Simplificar

2 cos (x) = 1

2 cos (x) = 1

Dividir ambos lados entre

2

2 cos (x) = 1

Dividir ambos lados entre

2

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

Simplificar

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

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

Soluciones generales para

cos (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}

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

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

Combinar toda las soluciones

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

Combinar toda las soluciones

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

Siendo que la ecuación esta indefinida para:

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

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

Ejemplos populares

2|sin(4θ)|=0

2 ∣ sin (4 θ) ∣ = 0

250sin(75)=393.19sin(45-θ)

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

tan(θ)= 6/(6.71)

tan (θ) = \frac{6}{6.71}

solvefor x,sin(x)-1=0 resolver para

x, sin (x) - 1 = 0

sin^2(θ)=1+cos(2θ)

sin^{2} (θ) = 1 + cos (2 θ)