Cos альфа = - 1/9
sin^2 alfa = 1 - cos^2 alfa
sin^2 alfa = 1 -1/81=80/81
1+tg^2alfa=1/cos^2alfa
1+tg^2alfa=1/1/81
1+tg^2alfa=81
tg^2alfa=80
1+ctg^2 alfa=1/sin^2alfa
1+ctg^2alfa=1/80/81
1+ctg^2alfa=81/80
ctg^2alfa=1/80
<span>2х+3у=6
2x=6-3y
x=(6-3y)/2
</span><span>2х+3у=6
3y=6-2x
y=(6-2x)/3</span>
Ответ с решением на фото.
1) sin x = -1; x = 3pi/2 + 2pi*k
x1 = 3pi/2 - 2pi = -pi/2; x2 = 3pi/2
2) cos x = 1/2; x = pi/3 + 2pi*k; x = -pi/3 + 2pi*k
x1 = -pi/3; x2 = pi/3; x3 = -pi/3 + 2pi = 5pi/3
3) tg x = √3; x = pi/3 + pi*k
x1 = pi/3 - 2pi = -5pi/3; x2 = pi/3 - pi = -2pi/3; x3 = pi/3; x4 = pi/3 + pi = 4pi/3
4) ctg x = -3; x = -arcctg(3) + pi*k ~ -0,32 рад + pi*k
x1 = -arcctg(3); x2 = -arcctg(3) + pi; x3 = -arcctg(3) + 2pi
5) 2sin^2 x - 7sin x + 5 = 0
(sin x - 1)(2sin x - 5) = 0
sin x = 5/2 - решений нет
sin x = 1; x = pi/2 + 2pi*k
x1 = pi/2 - 2pi = -3pi/2; x2 = pi/2