hhbhy1985
幼苗
共回答了21个问题采纳率：100% 举报
y=sin²x+2sinxcosx+3cos²x
=(1-cos2x)/2+sin2x+3(1+cos2x)/2
=sin2x+cos2x+2
=√2sin(2x+π/4)+2
(1)值域[2-√2,2+√2]
(2)增区间
2kπ-π/2≤2x+π/4≤2kπ+π/2
2kπ-3π/4≤2x≤2kπ+π/4
kπ-3π/8≤x≤kπ+π/8
所以,增区间为[kπ-3π/8,kπ+π/8],k∈Z,同理,减区间为[kπ+π/8,kπ+5π/8],k∈Z
1年前
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