Đáp án:
`a, y_{max}=3 <=> x= π/4 + k2π \ (k \in ZZ)`
`y_{min} = -1 <=> x= -(3π)/4 + k2π \ (k \in ZZ)`
`b, y_{max} = 2\sqrt{2} -3<=> x = k2π \ (k \in ZZ)`
+ `y_{min} = -3 <=> x = π+ k2π \ (k \in ZZ)`
Giải thích các bước giải:
`a, y= 2sin (x +π/4) +1`
Có: `-1≤ sin(x +π/4) ≤1`
`<=> -2 ≤ 2sin (x +π/4) ≤2`
`<=> -1 ≤ 2sin (x +π/4) +1≤3`
+ `y_{max} = 3`
`<=> sin(x +π/4) =1`
`<=> x +π/4 = π/2 +k2π \ (k \in ZZ)`
`<=> x = π/4 + k2π \ (k \in ZZ)`
+ `y_{min} = -1`
`<=> sin (x +π/4)=-1`
`<=> x +π/4 = -π/2 +k2π \ (k \in ZZ)`
`<=> x = -(3π)/4 +k2π \ (k \in ZZ)`
________________________________
`b, y= 2 \sqrt{cos x +1 } -3`
Có: `- 1 ≤ cos x ≤ 1`
`<=> 0 ≤ cos x +1 ≤2`
`<=> 0 ≤ 2\sqrt{cos x +1} ≤ 2\sqrt{2}`
`<=> -3 ≤ 2\sqrt{cos x +1 } -3 ≤ 2\sqrt{2} -3`
+ `y_{max} = 2\sqrt{2} -3`
`<=> cos x = 1<=> x = k2π \ (k \in ZZ)`
+ `y_{min} = -3`
`<=> cos x = -1 <=> x = π+ k2π \ (k \in ZZ)`
