1) Sin60 = sqrt(3)/2, cos585 = cos(585-360) = cos225 = -1/sqrt(2), tg135 = -tan(45) = -1sqrt(3)/2 * (-1/sqrt(2)) - (-1) = -sqrt(3)/2 + 1
2) sin(11П/6) = sin(П/6) = 1/2, tg(-5П/4) = tg(П/4) = 1, cos(-11П/6) = cos(П/6) = sqrt(3)/21/2 * 1 + sqrt(3)/2 = sqrt(3)/2 + 1/2
3) sina = -5/13 (x = 3П/2)cosa = sqrt(1 - (-5/13)^2) = 12/13tga = sina/cosa = (-5/13) / (12/13) = -5/12ctga = 1/tga = -12/5
4) а) 2sin^2a - 1 - tgactga = 2(-5/13)^2 - 1 - (-5/12 * -12/5) = 0б) (sin(3П/2)-a)/cos(2П+a) = -1/cos(a) = -1/cosa
5) sqrt(3)sina + 2sin(П/6-a) = sqrt(3)(-5/13) + 2sin(П/6 - a)= -5sqrt(3)/13 + 2(1/2 * cos(a) - sin(a)/2) = -5sqrt(3)/13 + cos(a) - sin(a)
6) 2cosx + sqrt(2) = 0cosx = -sqrt(2)/2x = 5П/4 + 2Пn, n ∈ Z
1) Sin60 = sqrt(3)/2, cos585 = cos(585-360) = cos225 = -1/sqrt(2), tg135 = -tan(45) = -1
sqrt(3)/2 * (-1/sqrt(2)) - (-1) = -sqrt(3)/2 + 1
2) sin(11П/6) = sin(П/6) = 1/2, tg(-5П/4) = tg(П/4) = 1, cos(-11П/6) = cos(П/6) = sqrt(3)/2
1/2 * 1 + sqrt(3)/2 = sqrt(3)/2 + 1/2
3) sina = -5/13 (x = 3П/2)
cosa = sqrt(1 - (-5/13)^2) = 12/13
tga = sina/cosa = (-5/13) / (12/13) = -5/12
ctga = 1/tga = -12/5
4) а) 2sin^2a - 1 - tgactga = 2(-5/13)^2 - 1 - (-5/12 * -12/5) = 0
б) (sin(3П/2)-a)/cos(2П+a) = -1/cos(a) = -1/cosa
5) sqrt(3)sina + 2sin(П/6-a) = sqrt(3)(-5/13) + 2sin(П/6 - a)
= -5sqrt(3)/13 + 2(1/2 * cos(a) - sin(a)/2) = -5sqrt(3)/13 + cos(a) - sin(a)
6) 2cosx + sqrt(2) = 0
cosx = -sqrt(2)/2
x = 5П/4 + 2Пn, n ∈ Z