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Popular >

sin(2x)+3cos^2(x)sin(x)=0

Solución

sin (2 x) + 3 cos^{2} (x) sin (x) = 0

Solución

x = 2 πn, x = π + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 2.30052 \dots + 2 πn, x = - 2.30052 \dots + 2 πn

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 131.81031 \dots^{\circ} + 36 0^{\circ} n, x = - 131.81031 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

sin (2 x) + 3 cos^{2} (x) sin (x) = 0

Re-escribir usando identidades trigonométricas

sin (2 x) + 3 cos^{2} (x) sin (x)

Utilizar la identidad trigonométrica del ángulo doble:

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

= 2 sin (x) cos (x) + 3 cos^{2} (x) sin (x)

2 cos (x) sin (x) + 3 cos^{2} (x) sin (x) = 0

Factorizar

2 cos (x) sin (x) + 3 cos^{2} (x) sin (x) : sin (x) cos (x) (3 cos (x) + 2)

2 cos (x) sin (x) + 3 cos^{2} (x) sin (x)

Aplicar las leyes de los exponentes:

a^{b + c} = a^{b} a^{c}

sin (x) cos^{2} (x) = sin (x) cos (x) cos (x)

= 2 sin (x) cos (x) + 3 sin (x) cos (x) cos (x)

Factorizar el termino común

sin (x) cos (x)

= sin (x) cos (x) (2 + 3 cos (x))

sin (x) cos (x) (3 cos (x) + 2) = 0

Resolver cada parte por separado

sin (x) = 0 or cos (x) = 0 or 3 cos (x) + 2 = 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

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

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

3 cos (x) + 2 = 0

Mover

2

al lado derecho

3 cos (x) + 2 = 0

Restar

2

de ambos lados

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

Simplificar

3 cos (x) = - 2

3 cos (x) = - 2

Dividir ambos lados entre

3

3 cos (x) = - 2

Dividir ambos lados entre

3

\frac{3 cos ( x )}{3} = \frac{- 2}{3}

Simplificar

cos (x) = - \frac{2}{3}

cos (x) = - \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (x) = - \frac{2}{3}

Soluciones generales para

cos (x) = - \frac{2}{3}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

Mostrar soluciones en forma decimal

x = 2 πn, x = π + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 2.30052 \dots + 2 πn, x = - 2.30052 \dots + 2 πn

Ejemplos populares

4sqrt(3)=8sin(θ)

43 = 8 sin (θ)

7tan(3x)=7

7 tan (3 x) = 7

sin(θ)=((0.0543)/(0.9911))

sin (θ) = (\frac{0.0543}{0.9911})

sin(x)=0.2419

sin (x) = 0.2419

(-1-3cos(x))^2+cos^2(x)=1

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