1) sin (x- π)=0
4
x-π =πn
4
x=π +πn
4
2) sin (10x -π)=1
3
10x-π = π +2πn
3 2
10x=π + π + 2πn
2 3
10x =3π+2π + 2πn
6
10x = 5π +2πn
6
x=5π : 10 + 2πn : 10
6
х=5π + 2πn
6*10 10
x= π + πn
12 5
3) sin (x + π)=-1
5 4
x + π = -π +2πn
5 4 2
x = -π - π +2πn
5 2 4
x =-2π-π + 2πn
5 4
x =-3π + 2πn
5 4
x=-3π*5 +2πn * 5
4 4
x=-15π +5πn
4 4
4) 4sin²x - 5sinx+1=0
Пусть y=sinx
4y²-5y+1=0
D=25-4*4-*1=9
y₁=5-3 = 1
8 4
y₂=1
sinx=¹/₄
x₁=(-1)^n * arcsin ¹/₄ +2πn
sinx=1
x₂=π +2πn
2
5) sin7x - sinx=0
2sin 7x-x cos7x+x=0
2 2
2sin3x cos4x=0
sin3x cos4x=0
sin3x=0 cos4x=0
3x=πn 4x=πn
x₁=πn x₂=πn
3 4