Вычислите значение выражения.

1) arcsin 0

2) arccos 1

3) arcsin√2/2

4) arccos 3

5) arcsin (-1)

6) arccos (-√3/2)

7) arctg 0

8) arctg 1

9) arctg (-√3)

10) arcctg (-√3/3)

11) arcsin (-1/2) + arccos 1

12) arcsin - 1/2 + arccos 1

13) cos (arccos 1)

14) sin (arcsin√2/2)

15) arcsin (sin пи/4)

16) arccos (cos (-пи/4))

17) cos (arcsin (-1/3))

18) tg (arccos (-1/4))

19) sin (arcctg (-2))

20) arcsin (cos пи/9)

1) arcsin 0 = 0

2) arccos 1 = 0;

3) arcsin√2/2 = π/4;

4) arccos 3 не существует угол косинус которой = 3;

5) arcsin (-1) = - π/2;

6) arccos (-√3/2) = π - π/6 = 5π/6;

7) arctg 0 = 0;

8) arctg 1 = π/4;

9) arctg (-√3) = - π/3;

10) arcctg (-√3/3) = π - π/3 = 2π/3;

11) arcsin (-1/2) + arccos 1 = - π/6 + 0 = - π/6;

12) (arcsin - 1) / 2 + arccos 1 = - π/4+0 = - π/4;

13) cos (arccos 1) = 1;

14) sin (arcsin√2/2) = √2/2;

15) arcsin (sin π/4) = arcsin (√2/2) = π/4;

16) arccos (cos ( - π/4)) = arccos (cos (π/4)) = arccos (√2/2)) = π/4;

17) cos (arcsin (-1/3)) = cos (arccos (√8/3) = √8/3 = 2√2/3;

18) tg (arccos (-1/4)) = tq (arctq (-√15) = - √15; 1+tq²α = 1/cos²α

19) sin (arcctg (-2)) = sin (arcsin (1/√5) = 1/√5;

20) arcsin (cos π/9) = arcsin (sin (π/2 - π/9)) = arcsin (sin7π/18) = 7π/18.