Область значения и определения y=2cos (x-п/3)

Решение

1. Область определения

y = 2cos (x-п/3)

D (y) = R

2. Область значения

- 1 ≤ 2cos (x-п/3) ≤ 1

- 1/2 ≤ cos (x-п/3) ≤ 1/2

1) cos (x-п/3) ≥ - 1/2

- arccos (-1/2) + 2πk ≤ x - п/3 ≤ arccos (-1/2) + 2πk, k ∈ Z

- 2π/3 + 2πk ≤ x - п/3 ≤ 2π/3 + 2πk, k ∈ Z

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

- π/3 + 2πk ≤ x ≤ π + 2πk, k ∈ Z

2) cos (x-п/3) ≤ - 1/2

arccos (-1/2) + 2πk ≤ x - п/3 ≤ 2π - arccos (-1/2) + 2πk, k ∈ Z

2π/3 + 2πk ≤ x - п/3 ≤ 2π - 2 π/3 + 2πk, k ∈ Z

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

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

π + 2πk ≤ x ≤ 5π/3 + 2πk, k ∈ Z