§ 30: 30.40

30.40 Обчисліть значення виразу:

1) arcsin(sin4π7) = arcsin(sin(π – 3π7)) = arcsin(sin3π7) = 3π7;

2) arcsin(sin3) = arcsin(sin(π – (π – 3))) = arcsin(sin(π – 3)) = π – 3;

3) arcsin(cos8) = arcsin(cos(5π2 – (5π2 – 8))) = arcsin(sin(5π2 – 8)) = 5π2 – 8.

4) arctg(tg10π13) = 10π13 ∉ (–π2; π2), але 10π13 – π ∉ (–π2; π2) = arctg(tg(10π13 – π)) = arctg(tg(–3π13)) = –10π13;

5) arctg(tg 5) = 5 ∉ (–π2; π2), але 5 – 2π ∈ (–π2; π2) = arctg(tg(5 – 2π)) = 5 – 2π;

6) arctg(ctg(13π21)) = arctg(tg(π2 – 13π21)) = arctg(tg(–5π42)) = –5π42;