问题描述: 已知函数f(X)=sin(x+π\3)-根号3cos(2π\3-x)(1)求函数最小正周期.(2)求函数在区间【-π\2,π\2]上的最大值与最小值 1个回答 分类:数学 2014-11-09 问题解答: 我来补答 f(x)=sin(x+π/3)-√3cos(2π/3-x)=sin(x+π/3)+√3cos[π-(2π/3-x)] =sin(x+π/3)+√3cos(x+π/3)=2[1/2×sin(x+π/3)+√3/2×cos(x+π/3)] =2sin[(x+π/3)+π/3]=2sin[(x+2π/3)(1)T=2π(2)∵x∈[﹣π/2,π/2] ∴x+2π/3∈[π/6,7π/6] ∴sin[(x+2π/3)∈[﹣1/2,1] ∴f(x)∈[﹣1,2] ∴最大值为2,最小值为﹣1 展开全文阅读