已知函数∫(x)=2√3sinxcosx+2cos2x-1(x∈R)
(1)求函数∫(x)的最小正周期及在区间[0,π/2]上的最大值和最小值;
(2)若∫(x0)=6/5,x0∈[π/4,π/2],求cos2x0的值
人气:274 ℃ 时间:2020-04-08 20:41:22
解答
1f(x)=2√3sinxcosx+2cos2x-1=√3sin2x+cos2x=2sin(2x+π/6)最小正周期T=2π/2=π∵x∈[0,π/2]∴2x+π/6∈[π/6,7π/6]∴2x+π/6=π/2时,f(x)max=22x+π/6=7π/6时,f(x)min=-12 f(x0)=6/5 ,即 2sin(2x0+π/6)=6/5...
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