Question

已知α为锐角,且m=sinα+cosα，求m的取值

绝对反对复制党

Answer 1

m=sinα+cosα
=√2*(√2/2*sinα+√2/2*cosα)
=√2*(sinαcosπ/4+cosαsinαπ/4)
=√2*sin(α+π/4)

α为锐角
0<α<π/2
π/4<α+π/4<3π/4
√2/2<sin(α+π/4)<=1
1<√2*sin(α+π/4)<=√2

所以1<m<=√2

Answer 2

m=sinα+cosα
=根号2(sinαcos45°+cosαsin45°)
=根号2sin(α+45°)
因为α为锐角
(根号2)/2<sin(α+45°)≤1
所以：1<m≤根号2