已知Y=½cos²x+二分之根号三×sinxcosx+1,求值域,周期和单调区间
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已知Y=½cos²x+二分之根号三×sinxcosx+1,求值域,周期和单调区间
已知Y=½cos²x+二分之根号三×sinxcosx+1,求值域,周期和单调区间
已知Y=½cos²x+二分之根号三×sinxcosx+1,求值域,周期和单调区间
y=1/2cos^2(x)+√3/2sinxcosx+1
=1/4(1+cos2x)+√3/4sin2x+1
=√3/4sin2x+1/4cos2x+5/4
=1/2[(sin2x)(√3/2)+(cos2x)(1/2)]
=1/2sin(2x+π/6)
1)
值域:【-1/2,1/2】
2)
T=2π/2=π
3)
(i)由-π/2+2kπ≤2x+π/6≤π/2+2kπ得单调增区间:
【-π/3+kπ,π/6+kπ】
(ii)由π/2+2kπ≤2x+π/6≤3π/2+2kπ得单调减区间:
【π/6+kπ,2π/3+kπ】