Question

已知函数f（x）=cos²x＋sinx.cosx＋3/2,x∈R.⑴求f（x）的小正周期及f（π/8）的值；

Answer 1

f(x)=(1+cos2x)/2+(1/2)sin2x+3/2

=(1/2)sin2x+(1/2)cos2x+2

=(√2/2)sin(2x+π/4)+2

(1)T=2π/2=π,f(π/8)=(√2/2)+2

(2)2kπ-π/2≤2x+π/4≤2kπ+π/2

得：kπ-3π/8≤x≤kπ+π/8

∴递增区间为：[kπ-3π/8,kπ+π/8],k∈Z