Eng sodda trigonometrik tenglamalar

a ∈ [−1; 1] sonning arksinusi — sinusi a ga teng bo‘lgan [−π/2; π/2] kesmadagi son; arkkosinusi — kosinusi a ga teng bo‘lgan [0; π] kesmadagi son; har qanday a ning arktangensi — tangensi a ga teng bo‘lgan (−π/2; π/2) oraliqdagi son. Masalan, arcsin(1/2) = π/6, arccos(−1/2) = 2π/3, arctg 1 = π/4. Tenglamalar: sin x = a (|a| ≤ 1) da x = (−1)ᵏ arcsin a + πk, k ∈ ℤ; cos x = a (|a| ≤ 1) da x = ± arccos a + 2πk, k ∈ ℤ; tg x = a da x = arctg a + πk, k ∈ ℤ. |a| > 1 bo‘lsa, sin x = a va cos x = a ning yechimi yo‘q, chunki sinus va kosinus [−1; 1] dan chiqmaydi. Maxsus hollar: sin x = 0 da x = πk, sin x = 1 da x = π/2 + 2πk, sin x = −1 da x = −π/2 + 2πk; cos x = 0 da x = π/2 + πk, cos x = 1 da x = 2πk, cos x = −1 da x = π + 2πk. Murakkab argumentda belgilash olamiz: sin 3x = a uchun 3x ni t deb olib, so‘ng x ni topamiz.