Question

已知關于x的方程

2

sin(x+

π

4

)=k在[0，π]上有兩解，則實數k的取值范圍是______．

Answer 1

∵0≤x≤π，∴

π

4

≤x+

π

4

≤

5π

4

，∴-

2

2

≤sin(x+

π

4

)≤1，-1≤

2

sin(x+

π

4

)≤

2

．
又∵f（x）=

2

sin(x+

π

4

)=k在[0，π]上有兩解，∴1≤k＜

2

．
∴實數k的取值范圍是1≤k＜

2

．
故答案為1≤k＜

2

．