Question

a) sinx>½
б) cos2х ≥√3/2​

Answer 1

Відповідь:

SinX ≥ 1/2;

1/2 = Sin(π/6);

1/2 = Sin(5 * π/6);

SinX ≥ Sin(π/6) + 2 * π * n. n Є Z;

X ≥ (π/6) + 2 * π * n. n Є Z;

SinX ≤ Sin(5 * π/6) + 2 * π * n. n Є Z;

X ≤ 5 * π/6 + 2 * π * n. n Є Z;

(π/6) + 2 * π * n ≤ X ≤ 5 * π/6 + 2 * π * n. n Є Z;

Ответ: (π/6) + 2 * π * n ≤ X ≤ 5 * π/6 + 2 * π * n. n Є Z.

Cos(2 * X - π/6) ≥ -1/√2;

-1/√2 = -√2/2 = Cos(±3 * π/4);

(-3 * π/4) + 2 * π * n ≤  (2 * X – π/6) ≤ (3 * π/4) + 2 * π * n;

(-3 * π/4 + π/6) + 2 * π * n ≤ 2 * X ≤ (3 * π/4 + π/6) + 2 * π * n;

-7 * π/12 + 2 * π * n ≤ 2 * X ≤ 11 * π/12 + 2 * π * n;

-7 * π/24 + 2 * π * n ≤ X ≤ 11 * π/24 + 2 * π * n;

Ответ: -7 * π/24 + 2 * π * n ≤ X ≤ 11 * π/24 + 2 * π * n. n Є Z.

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