已知函数y=cos2x+sin方x-cosx

题目

已知函数y=cos2x+sin方x-cosx
（1）y的最大值与最小值；
（2）在[0,2π]范围内,函数取得最大值与最小值时的x的集合

答案

y = cos2x + sin²x - cosx= cos²x - cosx = (cosx - 1/2)² - 1/4x = 2kπ + π ,max(y) = 2x = 2kπ ± π/3 ,min(y) = -1/4x∈[0,2π]x ∈ {π} ,max(y) = 2x ∈ {π/3 ,8π/3} ,min(y) = -1/4