Заполните таблицы 5,6 10 0,89 560 83,4 890​

1) 2 sin x + 1 = 0
2 sin x = -1
sin x = -1/2
x = (-1) ^ n * (- п/6) + пn
2) tg (3x - п) = 0
3x - п = пn
3x = пn + п
х = пn/3 + п/3
3) 2 cos x + √3 = 0
2 cos x = - √3
Cos x = - √3/2
X = ±5π/6 + 2πn
4) 2 sin 2x = √3
Sin 2x = √3 / 2
2X = (-1)^n * π/3 + πn
X = (-1)^n * π/6 + πn/2
5) sin x - √3 cos x = 0
2 sin (x- π/3) = 0
Sin (x - π/3) = 0
X - π/3 = πn
X = π/3+ πn
6) tg 2x = 1
2x = π/4 + πn
X = π/8 + πn/2
7) 2 sin x = 1
Sin x = ½
X = (-1)^n * π/6 + πn
8) 8 sin ^ 2 x – 10 sin x – 7 =0
Замена sin x = t, -1 ≤ t ≤ 1
8 t^2 – 10 t – 7 =0
D = 100+7*8*4 = 324
T1 = (10 + 18) / 16 = 28/ 16 = 7/4 – не удовлетворяет условию замены
T2 = (10 - 18) / 16 = -8 / 16 = -1/2
Обратная замена:
Sin x = -1/2
X = (-1)^n *(-π/6) + πn
9)4 sin 2x + 10 cos 2x = 1
2 √29 sin (2x +arctg 5/2) = 1
sin (2x +arctg 5/2) = 1 / 2 √29
2x +arctg 5/2 = (-1) ^n * arcsin (1 / 2 √29) + πn
2x = (-1) ^n * arcsin (1 / 2 √29) + πn - arctg 5/2
X = (-1) ^n * arcsin (1 / 2 √29)/2 + πn/2 – (arctg 5/2) / 2

1.(2 5/18 - 5 1/12 + 1 2/9) * (0,81 : 0,4) = ( 2 10/36 - 5 3/36 + 1 8/36) *(8.1 : 4)=(3 18/36 -5 3/36)* 2.025= - ( 5 3/36 - 3 18/36)* 2.025=
- (4 39/36 - 3 18/36)*2.025= (- 1 21/36)*2.025=(- 1 7/12)*2.025=
= - (19/12)*2.025=- 3.20625

2.-1,5 : 0,5 * (3 8/15 - 4 1/18 - 1 1/5) = -15 : 5* ( 3 48/90 - 4 5/90- 1 18/90)=
-3 * (3 48/90 -5 23/90)= -3* (- (5 23/90-3 48/90)= + 3 * (4 113/90 - 3 48/90)=+3*(1 65/90)=+3*(1 13/18)=3*1+3*(13/18)=3+13/6=3+2 1/6=5 1/6

3. -3,075 : 1,5 + 0,5 * (0,04 - 3 4/25) = -2.05 +0.5 *(0.04 - 3.16)=-2.05 -0.5*3.12=-2.05-1.56=-3.61

4.(0,0612 : 0,6 - 2/5) x 0,5 - 0,5= (0.102 -0.4)*0.5-0.5= - 0.298*0.5 - 0.5= -0.149 - 0.5= - 0.649