Решите неравенство:

а) cos x≥√3/2

б) tg (x/3-1) ≤-1

Решение

а) cos x ≥ √3/2

- arccos (√3/2) + 2πn ≤ x ≤ arccos (√3/2) + 2πn, n∈Z

5π/6 + 2πn ≤ x ≤ π/6 + 2πn, n∈Z

б) tg (x/3 - 1) ≤ - 1

- π/2 + πk ≤ (x/3 - 1) ≤ arctg (-1) + πk, k∈z

- π/2 + πk ≤ (x/3 - 1) ≤ - π/4 + πk, k∈z

- π/2 + 1 + πk ≤ (x/3) ≤ - π/4 + 1 + πk, k∈z

- 3π/2 + 3 + 3πk ≤ x ≤ - 3π/4 + 3 + 3πk, k∈z