Question

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)

Answer 1

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 .

Answer 2

1. arcsin 0 = 0
2. arccos 1 = 0
3. arcsin (√2/2) = π/4 (or 45 degrees)
4. arccos 3 is undefined since the range of arccosine function is limited to [-1, 1], and 3 is outside this range.
5. arcsin (-1) = -π/2 (or -90 degrees)
6. arccos (-√3/2) = 5π/6 (or 150 degrees)
7. arctg 0 = 0
8. arctg 1 = π/4 (or 45 degrees)
9. arctg (-√3) = -π/3 (or -60 degrees)
10. arcctg (-√3/3) = -π/6 (or -30 degrees)
11. arcsin(-1/2) + arccos 1 = -π/6 + 0 = -π/6 (or -30 degrees)
12. arcsin (-1/2) + arccos 1 = -π/6 + 0 = -π/6 (or -30 degrees)
13. cos(arccos 1) = cos(0) = 1
14. sin(arcsin (√2/2)) = sin(π/4) = √2/2
15. arcsin(sin (π/4)) = arcsin(√2/2) = π/4 (or 45 degrees)
16. arccos (cos (-π/4)) = arccos (√2/2) = π/4 (or 45 degrees)
17. cos(arcsin (-1/3)) = cos(-π/6) = √3/2
18. tg(arccos (-1/4)) = tg(π/3) = √3
19. sin(arcctg (-2)) = sin(-π/6) = -1/2
20. arcsin(cos(π/9)) = arcsin(√3/2) = π/3 (or 60 degrees)