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Popular >

3(2sin(x)-sqrt(2))(4cos(x)-2)=0

Solución

3 (2 sin (x) - 2) (4 cos (x) - 2) = 0

Solución

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

Grados

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Pasos de solución

3 (2 sin (x) - 2) (4 cos (x) - 2) = 0

Resolver cada parte por separado

2 sin (x) - 2 = 0 or 4 cos (x) - 2 = 0

2 sin (x) - 2 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

2 sin (x) - 2 = 0

Mover

2

al lado derecho

2 sin (x) - 2 = 0

Sumar

2

a ambos lados

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

Simplificar

2 sin (x) = 2

2 sin (x) = 2

Dividir ambos lados entre

2

2 sin (x) = 2

Dividir ambos lados entre

2

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

Simplificar

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

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

Soluciones generales para

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

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 = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

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

4 cos (x) - 2 = 0

Mover

2

al lado derecho

4 cos (x) - 2 = 0

Sumar

2

a ambos lados

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

Simplificar

4 cos (x) = 2

4 cos (x) = 2

Dividir ambos lados entre

4

4 cos (x) = 2

Dividir ambos lados entre

4

\frac{4 cos ( x )}{4} = \frac{2}{4}

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 = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Ejemplos populares

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

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

sqrt(3)tan(θ)-2sin(θ)tan(θ)=0

3 tan (θ) - 2 sin (θ) tan (θ) = 0

(sin(2x))/(sin(x))=1.5

\frac{sin ( 2 x )}{sin ( x )} = 1.5

solvefor x,yz=sin(xy)resolver para

x, yz = sin (x y)

sin^2(x)=((5m-5))/2

sin^{2} (x) = \frac{( 5 m - 5 )}{2}