求函数f(x)=sinxcosx+根号3cos平方x的值域和最小正周期

2025-12-17 19:11:31
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回答1:

f(x)=sinxcosx+√3cos^2 x=1/2*2sinxcosx+√3*(cos2x-1)/2=1/2sin2x+√3/2cos2x-√3/2=sin2xcosπ/3+cos2xsinπ/3-√3/2=sin(2x+π/3)-√3/2因为 1>=sin(2x+π/3)>=-1所以值域是 [1-√3/2,-1-√3/2]最小正周期是 T=2...