2sinx - 1 = 0 thuộc [-10;10]
<=> 2sinx = 1
<=> sinx = 1/2
<=> sin x = sin π/6
<=> x = π/6 + k2π
Hoac x = π - π/6 + k2π
<=> x = π/6 + k2π
Hoac x = 5π/6 + k2π
+ Ta co : -10 ≤ x ≤ 10
Th1 : -10 ≤ π/6 + k2π ≤ 10
<=> -10 ≤ π(1/6 + k2) ≤ 10
<=> -10/π ≤ 2(1/12 + k) ≤ 10/π
<=> -5/π ≤ 1/12 + k ≤ 5/π
<=> -5/π -1/12 ≤ k ≤ 5/π - 1/12
<=> -1,675 ≤ k ≤ 1,51
=> k = -1 => x = -11π/6
Hoac k = 0 => x = π/6
k = 1 => x = 13π/6
Th2 : -10 ≤ x ≤ 10
<=> -10 ≤ 5π/6 + k2π ≤ 10
<=> -10 ≤ π(5/6 + k2) ≤ 10
<=> -10/π ≤ 5/6 + 2k ≤ 10/π
<=> -10/π ≤ 2(5/12 + k ) ≤ 10/π
<=> -5/π ≤ 5/12 + k ≤ 5/π
<=> -5/π - 5/12 ≤ k ≤ 5/π - 5/12
<=> -2,01 ≤ k ≤ 1,175
=> k = -2 => x = -19π / 6
Hoac k = -1 => x = -7π/6
k = 0 => x = 5π/6
k = 1 => x = 17π / 6
Vậy nghiệm của phương trình là : x = -11π/6 ; x = π/6 ; x = 13π/6 ; x = -19π / 6 ; x = -7π/6 ; x = 5π/6 ;
x = 17π / 6