已知函数f(x)=1/2sinx+√3/2cosx(1)求f(x)的单调增区间(2)解不等式f(x)大于等于1/2
问题描述:
已知函数f(x)=1/2sinx+√3/2cosx
(1)求f(x)的单调增区间
(2)解不等式f(x)大于等于1/2
答
f(x)=1/2sinx+√3/2cosx=sin(x+π/3)
∴单调增区间(2kπ-5π/6,2kπ+π/6)
f(x)=sin(x+π/3)≥1/2
∴x+π/3∈[2kπ+π/6,2kπ+5π/6]
∴x∈[2kπ-π/6,2kπ-π/2]