已知y=(sinx+cosx)^+2cos^x求递减区间,求最大值最小值
问题描述:
已知y=(sinx+cosx)^+2cos^x求递减区间,求最大值最小值
如题,^为平方
答
y=(sinx+cosx)^2+2cos^x=2+sin2x+cos2x=2+√2sin(2x+π/4)y max=2+√2,y min=2-√2.2kπ+π/2≤2x+π/4≤2kπ+3π/22kπ+π/4≤2x≤2kπ+5π/4kπ+π/8≤x≤kπ+5π/8它的递减区间[kπ+π/8,kπ+5π/8],k∈Z....