已知函数f(x)=2sinx^2+2根号3sinxcosx+1,求f(x)的最小正周期及对称中心,若x∈[-π/6,π/3]
(1)求f(x)的最小正周期及对称中心
(2)若x∈[-π/6,π/3],求f(x)的最大值和最小值
人气:270 ℃ 时间:2020-04-26 10:56:46
解答
1、f(x)=1-cos2x+√3sin2x+1=2sin(2x- π/6)+2=2sin[2(x-π/12)]+2,f(x)的最小正周期T=2π/2=π,作出函数图像,从图中可知,对称中心为:(π/3+kπ/2,2),k∈Z,2、在区间[-π/6,π/3]中,函数从最小值到最大值,在x=-...
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