Найдите нули и область значений функции f (x) = sin (11x/15) - 1/2

Находим нули функции:

f (x) = sin (11x/15) - 1/2

sin (11x/15) - 1/2=0

sin (11x/15) = 1/2

11x/15 = (-1) ⁿ*π/6+πn, n∈Z

x = (-1) ⁿ*15π / (11*6) + 15πn/11, n∈Z

x = (-1) ⁿ*5π/22 + 15πn/11, n∈Z

Находим область значений функции:

f (x) = sin (11x/15) - 1/2

E (sinx) = [-1; 1]

E (sin (11x/15)) = [-1; 1]

E (sin ((11x/15) - 1/2) = [-1-1/2; 1-1/2]

E (sin ((11x/15) - 1/2) = [-1,5; 0,5]