已知函數(shù)y=(sinx+cosx)^2+2cos^2x（1）當(dāng)y取的最大值時(shí),求自變量X的取值集合（2）該函數(shù)圖像可由y=sinx(x屬于R）的圖像經(jīng)過怎樣的變換得到的?麻煩詳細(xì)過程
解析：y=(sinx+cosx)^2+2cos^2x=sin2x+cos2x+2=√2sin(2x+π//4)+2
2x+π//4=2kπ+π/2==>x=kπ+π/8
當(dāng)y取的最大值時(shí),求自變量X的取值集合x=kπ+π/8
由y=sinx==>y=√2sin(2x+π//4)+2
(1)將Y坐標(biāo)伸長√2倍,得y=√2sinx
(2)y=√2sinx水平左移π//4個(gè)單位,得y=√2sin(x+π//4)
(3)將X坐標(biāo)縮小到原來的1/2,得y=√2sin(2x+π//4)
(4)將y=√2sin(2x+π//4)圖像上移2個(gè)單位,得y=√2sin(2x+π//4)+2圖像.