Задача 45275 ...

sova

2020-03-24 09:27:30

★

a)
arccos(-0,5)=2π/3, так как cos(2π/3)=-0,5; (2π/3) ∈ [0;π]

arcsin(-0,5)=-π/6;так как sin(-π/6)=-0,5; (-π/6) ∈ [-π/2;π/2]

[b]arccos(-0,5)+arcsin(-0,5)=(2π/3)+(-π/6)=(4π/6)-(π/6)=3π/6=π/2[/b]

б)
arccos(-sqrt(2)/2)=3π/4, так как cos(3π/4)=-sqrt(2)/2 и (3π/4) ∈[0;π]
arcsin(-1)=-π/2; так как sin(-π/2)=-1; (-π/2) ∈ [-π/2;π/2]

[b]arccos(-sqrt(2)/2) - arcsin(-1)= (3π/4)-(-π/2)=5π/4[/b]
в)
arccos(-sqrt(3)/2)=5π/6, так как cos(5π/6)=-sqrt(3)/2 и (5π/6) ∈ [0;π]
arcsin(-sqrt(3)/2)=-π/3, так как sin(-π/3)=-sqrt(3)/2; (-π/3) ∈ [-π/2;π/2]

[b]arccos(-sqrt(3)/2)+arcsin(-sqrt(3)/2)=(5π/6)+(-π/3)=(5π/6)-(2π/6)=3π/6=π/2
[/b]

г)
arccos(sqrt(2)/2)=π/4, так как cos(π/4)=sqrt(2)/2 и (π/4) ∈[0;π]
arcsin(sqrt(3)/2)=π/3, так как sin(π/3)=sqrt(3)/2; (π/3) ∈ [-π/2;π/2]

[b]arccos(sqrt(2)/2)-arcsin(sqrt(3)/2)=(π/4)-(π/3)=-π/12[/b]