8sin^4(x)-3sin^2(x)+1/4 =0

Solución

8 sin^{4} (x) - 3 sin^{2} (x) + \frac{1}{4} = 0

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = 0.36136 \dots + 2 πn, x = π - 0.36136 \dots + 2 πn, x = - 0.36136 \dots + 2 πn, x = π + 0.36136 \dots + 2 πn

Pasos de solución

8 sin^{4} (x) - 3 sin^{2} (x) + \frac{1}{4} = 0

Usando el método de sustitución

sin (x) = \frac{1}{2}, sin (x) = - \frac{1}{2}, sin (x) = \frac{2}{4}, sin (x) = - \frac{2}{4}

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

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

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

Combinar toda las soluciones

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = arcsin (\frac{2}{4}) + 2 πn, x = π - arcsin (\frac{2}{4}) + 2 πn, x = arcsin (- \frac{2}{4}) + 2 πn, x = π + arcsin (\frac{2}{4}) + 2 πn

Mostrar soluciones en forma decimal

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = 0.36136 \dots + 2 πn, x = π - 0.36136 \dots + 2 πn, x = - 0.36136 \dots + 2 πn, x = π + 0.36136 \dots + 2 πn

- 2 cot (θ) = - 1 - cot^{2} (θ)

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

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

\frac{1 + csc ( y )}{cot ( y ) + cos ( y )} = csc (y)

2 = sin (10 x)