Решите неоавенство 6 sin^2x- sin x-1<0

Question

Решите неоавенство 6 sin^2x- sin x-1<0

Answer 1

6sin²x - sinx - 1 < 0
sinx = t
6t² - t - 1 < 0
D = 1 + 24 = 25
t = (1 - 5)/12 = - 1/3                  t = (1 + 5)/12 =  1/2
- 1/3 < t < 1/2
- 1/3 < sinx < 1/2
x ∈ (- arcsin (1/3) + 2πn ; π/6 + 2πn) ∪ (5π/6 + 2πn ; π + arcsin (1/3) + 2πn)