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sinx+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 x∈[-3p/2; 5p/2]

sinx+√3/2=0 x∈[-2p; 2p]

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