x ≈ 0,358 + k ⋅ 2 π ∨ x ≈ 2,784 + k ⋅ 2 π
x ≈ -0,358 + k ⋅ 2 π ∨ x ≈ -2,784 + k ⋅ 2 π
x = 1 3 π + k ⋅ 2 π ∨ x = 2 3 π + k ⋅ 2 π
x = 1 1 4 π + k ⋅ 2 π ∨ x = 1 3 4 π + k ⋅ 2 π
x = 1 2 π + k ⋅ 2 π
x = 1 + k ⋅ 2 π ∨ x = π - 1 + k ⋅ 2 π
x = sin ( 1 ) ≈ 0,841
2 sin ( x ) - 1 = 0 gives sin ( x ) = 1 2 and so x = 1 6 π ∨ x = 5 6 π ∨ x = 2 1 6 π ∨ x = 2 5 6 π . The zeroes are ( 1 6 π , 0 ) , ( 5 6 π , 0 ) , ( 2 1 6 π , 0 ) and ( 2 5 6 π , 0 ) .
1 6 π ≤ x ≤ 5 6 π ∨ 2 1 6 π ≤ x ≤ 2 5 6 π .
sin ( 2 x ) = 0,5 gives 2 x = 1 6 π + k ⋅ 2 π ∨ 2 x = 5 6 π + k ⋅ 2 π and so x = 1 12 π + k ⋅ π ∨ x = 5 12 π + k ⋅ π . On [ 0 , 4 π ] : x = 1 12 π ∨ x = 5 12 π ∨ x = 1 1 12 π ∨ x = 1 5 12 π ∨ x = 2 1 12 π ∨ x = 2 5 12 π ∨ x = 3 1 12 π ∨ x = 3 5 12 π .
1 12 π ≤ x ≤ 5 12 π ∨ 1 1 12 π ≤ x ≤ 1 5 12 π ∨ 2 1 12 π ≤ x ≤ 2 5 12 π ∨ 3 1 12 π ≤ x ≤ 3 5 12 π .