Обернені тригонометричні функції. Розв'язування найпростіших тригонометричних рівнянь

^{π ⁄ 2}

π ⁄ 4

0

2π

π ∕ 2

0

2π

π

π ∕ 2

π ⁄ 4

π

0

π

½

π ∕ 3

π ∕ 4

½

-1

π

π ⁄ 3

π ∕ 2

π ⁄ 3

π ⁄ 4

π

-π ∕ 2

-½

-π/6

-π/3

π/3

π/6

π

∛3

-1

-π

-π/4

3π/4

π/3

π/6

5π/6

2π/3

sin x =2/3

cos x =2/3

sin x =3/2

tg x = 3/2

4πk, k∊Z

2πk, k∊Z

πk, k∊Z

π + 2πk, k∊Z

-π/12 + πk, k∊Z

π/12 + πk, k∊Z

5π/12 + πk, k∊Z

7π/12 + πk, k∊Z

π/2 + πk, k∊Z

πk, k∊Z

π/6 + πk/3, k∊Z

πk/3, k∊Z

±π/4 + 2πk, k∊Z

±3π/4 + 2πk, k∊Z

±π/4 + πk, k∊Z

±3π/4 + πk, k∊Z

пk, k є z

2пk, k є z

arcsin (-2) + пk, k є z

Немає розв'язків

(-1)ⁿπ⁄18 +π⁄18+πn⁄3, n∊ℤ

(-1)ⁿπ⁄6 +π⁄6+πn, n∊ℤ

(-1)ⁿπ⁄8 +π⁄8+πn⁄4, n∊ℤ

(-1)ⁿπ⁄3 +π⁄3+πn, n∊ℤ

cosx = 1

tgx = - 1

sinx = √2 ∕ 2

tgx = √3

π ⁄₄

- π ∕₄

π ∕ ₂

π

tg x=5/2

sin x=5/2

cos x=2/5

ctg x=2/5

π/3

π/4

π/6

π/2

- π/3

- π/6

2π/3

5π/6

- π/4 + πn, n ∈ Z

π/4 + πn, n ∈ Z

3π/4 + πn, n ∈ Z

- π + πn, n ∈ Z

π/6 + 3πn, n ∈ Z

3π/2 + 3πn, n ∈ Z

2π/3 + 3πn, n ∈ Z

π/2 +πn, n ∈ Z

- π/12 + πn, n ∈ Z

π/12 + πn, n ∈ Z

- π/24 + π/2 n, n ∈ Z

- π/24 + 2πn, n ∈ Z

sin x=3/4

tg x=3/4

ctg x=4/3

cos x=4/3

-π/12 + πk, k∊Z

π/12 + πk, k∊Z

5π/12 + πk, k∊Z

7π/12 + πk, k∊Z

±π/4 + 2πk, k∊Z

±3π/4 + 2πk, k∊Z

±π/4 + πk, k∊Z

±3π/4 + πk, k∊Z

⁺⁄⁻ π ∕ 12+2πn, n∊ℤ

⁺⁄⁻ π ∕ 24+πn, n∊ℤ

⁺⁄⁻ π ∕ 4+2πn, n∊ℤ

⁺⁄⁻ π ∕ 3+2πn, n∊ℤ

пk, k є z

2пk, k є z

arcsin (-2) + пk, k є z

Немає розв'язків

(-1)ⁿπ⁄18 +π⁄18+πn⁄3, n∊ℤ

(-1)ⁿπ⁄6 +π⁄6+πn, n∊ℤ

(-1)ⁿπ⁄8 +π⁄8+πn⁄4, n∊ℤ

(-1)ⁿπ⁄3 +π⁄3+πn, n∊ℤ

πn, nєℤ

π/2+2πn, nєℤ

2πn, nєℤ

-π/2+2πn, nєℤ

(-1)^{n+1 π}/₆+πn,nєℤ

(-1)^{n π}/₃+πn,nєℤ

(-1)^{n π}/₆+πn,nєℤ

(-1)^{n+1 π}/₃+2πn,nєℤ

^π/₂+2πn,nєℤ

2πn,nєℤ

^3π/₂+2πn,nєℤ

^π/₂+πn,nєℤ

2π + 4πn, n∊Z

π/4 + πn, n∊Z

π/2 + πn, n∊Z

π + 2πn, n∊Z