Решение:
1. cos 6 = cos (2π - 6),
0 ≤ 2π -6 ≤ π, тогда
arccos(cos 6) = arccos(cos (2π - 6)) = 2π - 6;
2. sin 6 = sin (6 - 2π),
- π/2 ≤ 6 - 2π ≤ π/2, тогда
arcsin(sin 6) = arcsin(sin(6 - 2π)) = 6 - 2π.
3. arctg(tg 6) =
tg6 = tg(6 - 2π),
- π/2 < 6 - 2π < π/2, тогда
arctg(tg 6) =arctg(tg(6 - 2π)) = 6 - 2π.
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Решение:
1. cos 6 = cos (2π - 6),
0 ≤ 2π -6 ≤ π, тогда
arccos(cos 6) = arccos(cos (2π - 6)) = 2π - 6;
2. sin 6 = sin (6 - 2π),
- π/2 ≤ 6 - 2π ≤ π/2, тогда
arcsin(sin 6) = arcsin(sin(6 - 2π)) = 6 - 2π.
3. arctg(tg 6) =
tg6 = tg(6 - 2π),
- π/2 < 6 - 2π < π/2, тогда
arctg(tg 6) =arctg(tg(6 - 2π)) = 6 - 2π.