305. 1) arcsin(sin(3π/4)); 2) arcsin(sin(2π/3)); 3) arcsin(cos(5π/6)); 4) arcsin(cos(3π/4)); 5) arcsin(2 sin(π/6)); 6) arcsin((1/2) tg(π/4)).

Значение arcsin должно лежать в [−π/2; π/2].

1. sin(3π/4) = √2/2, поэтому arcsin(sin(3π/4)) = π/4.
2. sin(2π/3) = √3/2, поэтому arcsin(sin(2π/3)) = π/3.
3. cos(5π/6) = −√3/2, поэтому arcsin(cos(5π/6)) = −π/3.
4. cos(3π/4) = −√2/2, поэтому arcsin(cos(3π/4)) = −π/4.
5. 2 sin(π/6) = 1, поэтому arcsin(1) = π/2.
6. (1/2) tg(π/4) = 1/2, поэтому arcsin(1/2) = π/6.