f(x)=2sin(2x-pai/3)+1

问题描述:

f(x)=2sin(2x-pai/3)+1
求f(x)>0的集合
f(x)在[0,pai]上的递增区间和递减区间

sin(2x-π/3)>-1/2=sin(2kπ-π/6)=sin(2kπ+7π/6)
所以2kπ-π/62kπ+π/6kπ+π/12x∈{x|kπ+π/120-π/3sin增区间是(2kπ-π/2,2kπ+π/2)
所以-π/3-π/3003π/211π/12所以增区间(0,5π/6)(11π/12,π)
减区间(5π/6,11π/12)