Вычислите а) arcs in (-1: 2) б) cos ( 2 arcs in 1: 2) 17pi в)cos 3 г) tg 600
166
433
Ответы на вопрос:
a)) / 2) = -0.523598776arccos(-1) = 3.14159265)
б)
cos(arcsin(-1/2)-arcsin 1)
arcsin(-1/2) = -π/6
arcsin 1 = π/2
cos(arcsin(-1/2)-arcsin 1)=
= cos(-π/6-π/2)=
= cos(-4π/6) =
= cos(2π/3) =
= -1/2
в)sin (17 pi/3) cos (5pi/4) = 1/2{2sin(17pi/3) cos(5pi/4)}= 1/2{2 sin(6pi - pi/3) cos (pi +pi/4)= 1/2{ -2sin(pi/3) (- cos(pi/4)}= 1/2{2sin(pi/3) cos(pi/4)}= 1/2{ sin(pi/3+pi4) + sin(pi/3- pi/4)}= 1/2{ sin(7pi/12) +sin(pi/12}}= 1/2{ sin (105) + sin (15)}= 1/2{sin(90+15) + sin(15)}= 1/2{ cos(15) +sin(15)}= 1/2{cos(45-30) + sin(45-30)}=1/2[{cos(45)cos (30)+sin(45)sin(30)} + {sin(45)cos(30) - cos(45) sin(30)}]=1/2{2 (1/sqrt((3)/2 )= 1/2{sqrt(3/2)}
г)
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