Question

已知關(guān)于x的方程

2

sin(x+

π

4

)=k在[0，π]上有兩解，則實(shí)數(shù)k的取值范圍是

1≤k＜

2

．

Answer 1

分析：利用三角函數(shù)的圖象與性質(zhì)即可求出．

解答：解：∵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(shí)數(shù)k的取值范圍是1≤k＜

2

．
故答案為1≤k＜

2

．

點(diǎn)評(píng)：熟練掌握三角函數(shù)的圖象與性質(zhì)是解題的關(guān)鍵．