Question

若sinx+cosy=2/3,则cosx+siny的取值范围是多少?

Answer 1

因 (sinx+cosy)^2 + (cosx+siny)^2 = 2 + 2sinxcosy + 2cosxsiny = 2+2sin(x+y)

所以

(cosx+siny)^2 = 2+2sin(x+y) - 4/9 = 14/9 +2sin(x+y)

因为 －1≤sin(x+y)≤1

所以

0≤(cosx+siny)^2≤32/9

即 |cosx+siny|≤4√2/3

所以

cosx+siny的取值范围是：

-4√2/3≤cosx+siny≤4√2/3