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Popular >

(4sin(x)+1)(2sin(x)+1)=0

Solución

(4 sin (x) + 1) (2 sin (x) + 1) = 0

Solución

x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

Grados

x = - 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 194.47751 \dots^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Pasos de solución

(4 sin (x) + 1) (2 sin (x) + 1) = 0

Resolver cada parte por separado

4 sin (x) + 1 = 0 or 2 sin (x) + 1 = 0

4 sin (x) + 1 = 0 : x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

4 sin (x) + 1 = 0

Mover

1

al lado derecho

4 sin (x) + 1 = 0

Restar

1

de ambos lados

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

Simplificar

4 sin (x) = - 1

4 sin (x) = - 1

Dividir ambos lados entre

4

4 sin (x) = - 1

Dividir ambos lados entre

4

\frac{4 sin ( x )}{4} = \frac{- 1}{4}

Simplificar

sin (x) = - \frac{1}{4}

sin (x) = - \frac{1}{4}

Aplicar propiedades trigonométricas inversas

sin (x) = - \frac{1}{4}

Soluciones generales para

sin (x) = - \frac{1}{4}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

2 sin (x) + 1 = 0 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

2 sin (x) + 1 = 0

Mover

1

al lado derecho

2 sin (x) + 1 = 0

Restar

1

de ambos lados

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

Simplificar

2 sin (x) = - 1

2 sin (x) = - 1

Dividir ambos lados entre

2

2 sin (x) = - 1

Dividir ambos lados entre

2

\frac{2 sin ( x )}{2} = \frac{- 1}{2}

Simplificar

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2}

Soluciones generales para

sin (x) = - \frac{1}{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{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combinar toda las soluciones

x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Mostrar soluciones en forma decimal

x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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