已知f(x)=sinx+根号3cosx(x属于R),1求单调区间2求对称轴和对称中心

Question

已知f(x)=sinx+根号3cosx(x属于R),1求单调区间 2求对称轴和对称中心

Answer 1

1
f(x)=sinx+√3cosx
=2(1/2sinx+√3/2cosx)
=2(cosπ/3sinx+sinπ/3cosx)
=2sin(x+π/3)
x+π/3∈[-π/2+2kπ,π/2+2kπ] 即 x∈[-5π/6+2kπ,π/6+2kπ] 单调增
x+π/3∈[π/2+2kπ,3π/2+2kπ] 即 x∈[π/6+2kπ,7π/6+2kπ] 单调减 k∈z
2
对称轴:x+π/3=kπ 即x=-π/3+kπ
对称中心:x+π/3=π/2+kπ 即x=π/6+kπ k∈z