Question

已知函數(shù)f(x)=cos2x+2sinxcosx(x∈R).

(1)求函數(shù)f(x)的最小正周期和最大值；

(2)函數(shù)f(x)的圖象可由y=2sinx(x∈R)的圖象經(jīng)過怎樣的平移和伸縮變換得到？

Answer 1

解:(1)f(x)=cos2x+2sinxcosx=cos2x+sin2x=2(cos2x+sin2x)

=2sin(2x+)(x∈R).

∴T=π，f(x)_min=2.

(2)先將y=2sinx(x∈R)的圖像向左移個單位，得到y=2sin(x+)的圖像;再將y=2sin(x+)的圖像的橫坐標(biāo)變?yōu)樵瓉淼囊话�，縱坐標(biāo)不變，得到y=2sin(2x+)的圖像.

或先將y=2sinx(x∈R)的圖像的橫坐標(biāo)變?yōu)樵瓉淼囊话�，縱坐標(biāo)不變，得到函數(shù)y=2sin2x的圖像;再將y=2sin2x的圖像向左移個單位，得到y=2sin(2x+)的圖像.