Question

Решите тригонометрическое неравенство
cos(x/3+pi/3)<=cos5pi/3

Answer 1

cos(x/3 + π/3) ≤ cos(5π/3)
cos(x/3 + π/3) ≤ 1/2
arccos(1/2) + 2πn ≤ (x/3 + π/3) ≤ 2π - arccos(1/2) + 2πn, n∈Z
π/3+ 2πn ≤ (x/3 + π/3) ≤ 2π - π/3 + 2πn, n∈Z
π/3+ 2πn ≤ (x/3 + π/3) ≤ 5π/3 + 2πn, n∈Z
π/3 - π/3  + 2πn ≤ (x/3)  ≤ 5π/3 - π/3 + 2πn, n∈Z
2πn ≤ (x/3)  ≤ 4π/3  + 2πn, n∈Z
6πn ≤  x  ≤ 4π  + 6πn, n∈Z

Answer 2

Spasibo")