Найдите область определения функции:a) y=7+√sinx/2

б) y=10-√cos x/3

Решение

а) y = 7 + √sin (x/2)

sinx/2 ≥ 0

arcsin0 + 2πn ≤ x/2 ≤ π - arcsin0 + 2πn, n ∈ Z

2πn ≤ x/2 ≤ π + 2πn, n ∈ Z

4πn ≤ x ≤ 2π + 4πn, n ∈ Z

б) y = 10 - √cos (x/3)

cosx/3 ≥ 0

- arccos0 + 2πk ≤ x/3 ≤ arccos0 + 2πk, k ∈ Z

- π/2 + 2πk ≤ x/3 ≤ π/2 + 2πk, k ∈ Z

- 3π/2 + 6πk ≤ x ≤ 3π/2 + 6πk, k ∈ Z