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Popular >

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

Solución

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

Solución

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

+1

Grados

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Factorizar

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

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

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

Factorizar

sin (x)

de

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

:

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

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

Factorizar el termino común

sin (x)

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

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

Factorizar el termino común

2 cos (x) - 1

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

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

Resolver cada parte por separado

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

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

sin (x) + 1 = 0 : x = \frac{3 π}{2} + 2 πn

sin (x) + 1 = 0

Mover

1

al lado derecho

sin (x) + 1 = 0

Restar

1

de ambos lados

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

Simplificar

sin (x) = - 1

sin (x) = - 1

Soluciones generales para

sin (x) = - 1

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{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

Combinar toda las soluciones

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

Ejemplos populares

sec^2(x)=2tan(x)

sec^{2} (x) = 2 tan (x)

4sin^2(x)-8cos(x)+1=0

4 sin^{2} (x) - 8 cos (x) + 1 = 0

sec^{2} (θ) = 4

sin (a) = \frac{5}{13}

sin (θ) = \frac{- 1}{2}