Trigonometrik tengsizliklarni yechish formulalari

Trigonometrik tengsizliklarni yechish formulalari
1. sin x ≥ a, (|a|≤1)
arcsin a + 2πk ≤ x ≤ π-arcsin a + 2πk.
2. sin x ≤ a,  (|a|≤1)
-π-arcsin a + 2πk ≤ x ≤ arcsin a + 2πk.
3. cos x ≥ a,(|a|≤1)
-arccos a + 2πk ≤ x ≤ arccos a + 2πk.
4. cos x ≤ a,(|a|≤1)
arccos a + 2πk ≤ x ≤ 2π-arccos a + 2πk.
5. tg x ≥ a
arctg a+πk ≤ x ≤ π/2+πk.
6. tg x ≤ a
-π/2+πk ≤ x ≤ arctg a+πk.
7. ctg x ≥ a

πk ≤ x ≤ arcctg a+πk.
8. ctg x ≤ a
arcctg a+πk ≤ x ≤ πk.

Misol: sin x > 0.5 tengsizlikni yeching.
Yechish:
arcsin 0.5 + 2πk < x < π-arcsin 0.5 + 2πk,
π/6 + 2πk < x < 5π/6 + 2πk, k-butun son.
Javob: π/6 + 2πk < x < 5π/6 + 2πk, k-butun son.

Trigonometriya