Вычислить: a)2arcsin(-1/2)+3аrcctg(-√3/3)-4arccos√2/2 б) sin(arccos(-1)) в)...

Question

Вычислить:
a)2arcsin(-1/2)+3аrcctg(-√3/3)-4arccos√2/2
б) sin(arccos(-1))
в) ctg(arccos1/2)
г) cos(arctg(-5/12))

Answer 1

Вычислить:
a)2arcsin(-1/2)+3аrcctg(-√3/3)-4arccos√2/2= 2*(-π/6) + 3*2π/3 -4*π/4 =
=-π/3 +2π -π = 2π/3
б) sin(arccos(-1)) = Sinπ = 0
в) ctg(arccos1/2)= Ctgπ/3 = √3/3
г) cos(arctg(-5/12)) = Cos(  1/√(1 +25/144) = Сos(12/13)