Найпростіші тригонометричні рівняння та нерівності

x = (-1)^ⁿπ∕12+πη/2, η∈Ζ

x = (-1)ⁿ⁺¹π∕12+πη/2, η∈Ζ

x = −π/4+πη, η∊Ζ

x = (-1)ⁿ⁺¹π∕6+πη/2, η∈Ζ

x = (-1)ⁿ⁺¹π∕6+πη, η∈Ζ

(-π/8+πĸ; 3π/8+πκ), κ∊Ζ

(-π/4+πĸ; 3π/4+πκ), κ∊Ζ

(-π/4+2πĸ; 3π/4+2πκ), κ∊Ζ

(-π/8+2πĸ; 5π/8+2πκ), κ∊Ζ

(-π/8+πĸ; 5π/8+πκ), κ∊Ζ

3π/2

6π/3

4π/3

8π/3

2π/3

x = π/2+2πη, η∊Ζ

x = π²/2+2π²η, η∊Ζ

x = π/2+πη, η∊Ζ

x = 1/2+η, η∊Ζ

x = 1/2+2η, η∊Ζ

∅

x = ±3π/8+πη, η∊Ζ

x = ±π/8+πη, η∊Ζ

x = ±3π/4+2πη, η∊Ζ

x = ±π/4+πη, η∊Ζ

(−π/3+2πκ; π/3+2πκ) , κ∊Ζ

(−1/8+2κ; 1/6+2κ) , κ∊Ζ

(1/3+2κ; 7/3+2κ) , κ∊Ζ

(−1/3+κ; 1/3+κ) , κ∊Ζ

(−1/3+2κ; 1/3+2κ) , κ∊Ζ

cosx<-3/4

sinx≥0,2

arctgx≥2

tgx≤1/√3

arctgx≤1,2

x = πη, η∊Ζ

x = π/6+πη, η∊Ζ

x = -π/3+πη, η∊Ζ

x = π/6+2πη, η∊Ζ

x = π/4+πη, η∊Ζ

cos x = π/3

arccos x = −π/3

arcsin x = π

arctg x = 2

arcctg x = 3

cos x ≥ 3/2

cos x < −1

sin x > 1

tg x ≤ √3

arcsin x ≤ −π

(π/6+2πη; 5/6π+2πη), η∊Ζ

(−π/6+2πη; π/6π+2πη), η∊Ζ

(−π/6+2πη; 7/6π+2πη), η∊Ζ

(−π/6+πη; π/6+2πη), η∊Ζ

(π/6+πη; 5/6π+πη), η∊Ζ

sin x = −1

cos x = −2

arctg x = 1

tg x = 1

(cos x−1)/sin x = 0