Найти корниsinx+1/2=0 x[0;3p]sinx-1/2=0 x[-p/2;3p/2]sinx+2/2=0 x[-3p;0]sinx-2/2=0

1) sinx = -1/2;
x = (-1)^(n+1)* arcsin(-1/2) + pi*n;
x = (-1)^(n+1)* pi/6) + pi*n; n  Z

n = 0; x = -pi/6 [0;3p]
n = 1; x = pi/6 + pi = 7pi/6 [0;3p]
n = 2; x = -pi/6 + 2pi = 11pi/6  [0;3p]
n = 3; x = pi/6 + 3pi [0;3p]
Ответ:  x = 7pi/6  x = 11pi/6

2)  sinx = 1/2;
x = (-1)^(n)* arcsin1/2) + pi*n;
x = (-1)^(n)* pi/6)+ pi*n; n  Z

n = -1; x = -pi/6 - pi  [-p/2;3p/2]
n = 0; x = pi/6 [-p/2;3p/2]
n = 1; x = -pi/6 + pi = 5pi/6 [-p/2;3p/2]
n = 2; x = pi/6 + 2pi [-p/2;3p/2]
Ответ:  x = pi/6  x = 5pi/6 

3) sinx = -2/2;
x = (-1)^(n+1)* arcsin(-2/2) + pi*n;
x = (-1)^(n+1)* pi/4) + pi*n; n  Z

n = -4; x = -pi/4 - 4pi [-3p;0]
n = -3; x = pi/4 - 3pi = -11pi/4 [-3p;0]
n = -2; x = -pi/4 -2pi = -9pi/4 [-3p;0]
n = -1; x = pi/4 - pi = - 3pi/4 [-3p;0]
n = 0; x = -pi/4 [-3p;0]
n = 1; x = pi/4 + pi [-3p;0]
Ответ:  x = -11pi/4  x =  -9pi/4  x = pi/4 - pi  x = -pi/4

4)  sinx = 2/2;
x = (-1)^(n)* arcsin(2/2) + pi*n;
x = (-1)^(n)* pi/4)+ pi*n; n  Z

n = -2; x = pi/4 - 2pi = -7pi/4 [-3p/2;5p/2]
n = -1; x = -pi/4 - pi = - 5pi/4 [-3p/2;5p/2]
n = 0; x = pi/4 [-3p/2;5p/2]
n = 1; x = -pi/4 + pi = 3pi/4 [-3p/2;5p/2]
n = 2; x = pi/4 + 2pi = 9pi/4 [-3p/2;5p/2]
n = 3; x = -pi/4 + 3pi [-3p/2;5p/2]
Ответ:  x = -5pi/4  x = pi/4  x = 3pi/4  x = 9pi/4

5) sinx = -3/2;
x = (-1)^(n+1)* arcsin(-3/2) + pi*n;
x = (-1)^(n+1)* pi/3) + pi*n; n  Z

n = -2; x = -pi/3 - 2pi [-2p;2p]
n = -1; x = pi/3 - pi = -2pi/3;
n = 0; x = -pi/3 [-2p;2p]
n = 1; x = pi/3 + pi = 4pi/3 [-2p;2p]
n = 2; x = -pi/3 + 2pi = 5pi/3  [-2p;2p]
n = 3; x = pi/3 + 3pi [-2p;2p]
Ответ:  x = -2pi/3  x = -pi/3  x =4pi/3  x = 5pi/3