- 三角函数已知函数f(x)=sin^2x+2sinxcosx+3c
- 已知f(x)=sin^2x+2sinxcosx+3cos^2x x属于R
求，
1.函数的最大值寄取得最大值时变量x的集合
2.函数f(x)的单调期间
- 解：以下用p表示3.14
f(x)=sin^2x+2sinxcosx+3cos^2x =sin^2x+sin2x+3cos^2x
f(x)的导数=2sinxcosx+2cos2x-6sinxcosx=2cos2x- 4sinxcosx=2cos2x-2sin2x=2√2cos(2x+p/4)
(1) 由于-1<=cos(2x+p/4)<=1,则-2√2<=f(x) <=2√2
当cos(2x+p/4)=1时，（2x+p/4）=2kp
即x=-p/8+kp时，f(x)最大
(2)单增区间：-p+2kp<=(2x+p/4)<=2kp
即-5p/8+kp<=x<=-p/8+kp
同理有单减区间-p/8+kp<=x<=3p/8+kp