sin^3(a)=3sin(a)-4sin^3(a)

Solución

sin^{3} (a) = 3 sin (a) - 4 sin^{3} (a)

a = 2 πn, a = π + 2 πn, a = - 0.88607 \dots + 2 πn, a = π + 0.88607 \dots + 2 πn, a = 0.88607 \dots + 2 πn, a = π - 0.88607 \dots + 2 πn

Pasos de solución

sin^{3} (a) = 3 sin (a) - 4 sin^{3} (a)

Usando el método de sustitución

sin (a) = 0, sin (a) = - \frac{3}{5}, sin (a) = \frac{3}{5}

sin (a) = 0 : a = 2 πn, a = π + 2 πn

sin (a) = - \frac{3}{5} : a = arcsin (- \frac{3}{5}) + 2 πn, a = π + arcsin (\frac{3}{5}) + 2 πn

sin (a) = \frac{3}{5} : a = arcsin (\frac{3}{5}) + 2 πn, a = π - arcsin (\frac{3}{5}) + 2 πn

Combinar toda las soluciones

a = 2 πn, a = π + 2 πn, a = arcsin (- \frac{3}{5}) + 2 πn, a = π + arcsin (\frac{3}{5}) + 2 πn, a = arcsin (\frac{3}{5}) + 2 πn, a = π - arcsin (\frac{3}{5}) + 2 πn

Mostrar soluciones en forma decimal

a = 2 πn, a = π + 2 πn, a = - 0.88607 \dots + 2 πn, a = π + 0.88607 \dots + 2 πn, a = 0.88607 \dots + 2 πn, a = π - 0.88607 \dots + 2 πn

cos (3 x) = \frac{3}{2}

sin (θ) + 2 sin (θ) cos (θ) = 0

x, arcsin (y) - arccos (x) = 1

- 6 = - 2 + 8 sin (θ + \frac{π}{4})

0 = 12 cos (\frac{π}{3} x) + 8