§ 30: 30.41

30.41 Обчисліть значення виразу:

arcos(cos11π9) = 11π9 ∉ [0; π], але 2π – 11π9 ∈ [0; π] = arccos(cos(2π – 11π9)) = arcos(cos 7π9) = 7π9;

2) arcos(cos6,28) = 6,28 ∉ [0; π], але 2π – 6,28 ∈ [0; π] = arcos (cos(2π – 6,28)) = 2π – 6,28;

3) arcos(sin12) = arcos(cos(π2 – 12)) = π2 – 12 ∉ [0; π], але π2 – 12 + 4π ∈ [0; π] = arcos(cos(π2 – 12 + 4π)) = arcos(cos(9π2 – 12)) =

= 9π2 – 12.

2) arcctg(ctg15π11) = 15π11 ∉ (0; π), але 15π11 – π ∈ (0; π) = arcctg(ctg(15π11 – π)) = 15π11 – π = 4π11;

5) arcctg(tg10) = arcctg(ctg(π2 – 10)) = π2 – 10 ∈ (0; π), але π2 – 10 + 3π ∈ (0; π) = arcctg(ctg(7π2 – 10))7π2 – 10.