Question

已知函数f(x)=cos²x+sinxcosx.（1）求函数f(x)的最大值;

Answer 1

(1)

f(x)＝(1+cos2x)/2+(1/2)sin2x

＝(√2/2)sin(2x+π/4)+1/2.

∴sin(2x+π/4)＝1时,

y|min＝(1+√2)/2.

(2)

f(A/2+π/8)＝1,

∴(√2/2)sin[2(A/2+π/8)+π/8]+1/2＝1

→sin(A+3π/8)＝√2/2

→A+3π/8＝3π/4

→A＝3π/8.

∴三角形面积S＝(1/2)·3·3·sin(3π/8)