English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin^2(x)=6cos^2(x)

Solución

2 sin^{2} (x) = 6 cos^{2} (x)

Solución

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

Grados

x = 12 0^{\circ} + 18 0^{\circ} n, x = 6 0^{\circ} + 18 0^{\circ} n

Pasos de solución

2 sin^{2} (x) = 6 cos^{2} (x)

Restar

6 cos^{2} (x)

de ambos lados

2 sin^{2} (x) - 6 cos^{2} (x) = 0

Factorizar

2 sin^{2} (x) - 6 cos^{2} (x) : 2 (sin (x) + 3 cos (x)) (sin (x) - 3 cos (x))

2 sin^{2} (x) - 6 cos^{2} (x)

Reescribir

- 6

como

3 \cdot 2

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

Factorizar el termino común

2

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

Factorizar

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

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

Reescribir

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

como

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

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

Aplicar las leyes de los exponentes:

a = (a)^{2}

3 = (3)^{2}

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

Aplicar las leyes de los exponentes:

a^{m} b^{m} = (ab)^{m}

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

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

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

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

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

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

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

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

Resolver cada parte por separado

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

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

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

cos (x), cos (x) \neq = 0

\frac{sin ( x ) + 3 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplificar

\frac{sin ( x )}{cos ( x )} + 3 = 0

Utilizar la identidad trigonométrica básica:

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

tan (x) + 3 = 0

tan (x) + 3 = 0

Mover

3

al lado derecho

tan (x) + 3 = 0

Restar

3

de ambos lados

tan (x) + 3 - 3 = 0 - 3

Simplificar

tan (x) = - 3

tan (x) = - 3

Soluciones generales para

tan (x) = - 3

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 = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

sin (x) - 3 cos (x) = 0 : x = \frac{π}{3} + πn

sin (x) - 3 cos (x) = 0

Re-escribir usando identidades trigonométricas

sin (x) - 3 cos (x) = 0

Dividir ambos lados entre

cos (x), cos (x) \neq = 0

\frac{sin ( x ) - 3 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplificar

\frac{sin ( x )}{cos ( x )} - 3 = 0

Utilizar la identidad trigonométrica básica:

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

tan (x) - 3 = 0

tan (x) - 3 = 0

Mover

3

al lado derecho

tan (x) - 3 = 0

Sumar

3

a ambos lados

tan (x) - 3 + 3 = 0 + 3

Simplificar

tan (x) = 3

tan (x) = 3

Soluciones generales para

tan (x) = 3

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 = \frac{π}{3} + πn

x = \frac{π}{3} + πn

Combinar toda las soluciones

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

Ejemplos populares

1+cot^2(θ)=1.33

1 + cot^{2} (θ) = 1.33

solvefor x,r+s-6t=cos(2x+y)resolver para

x, r + s - 6 t = cos (2 x + y)

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

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

-2cos(θ/2)=0

- 2 cos (\frac{θ}{2}) = 0

cos(x)=-3/4 ,tan(x)is

cos (x) = - \frac{3}{4}, tan (x) i s