y=1/2cos²x+√3/2sinxcosx+1的增区间√是根号

y=1/2cos²x+√3/2sinxcosx+1的增区间√是根号
y=1/2cos²x+√3/2sinxcosx+1的增区间
√是根号

y=1/2cos²x+√3/2sinxcosx+1的增区间√是根号
y=1/2*cos²x+√3/2*sinxcosx+1
=1/4*(1+cos2x)+√3/4*sin2x+1
=1/2*(1/2*cos2x+√3/2*sin2x)+5/4
=1/2*sin(2x+π/6)+5/4
令2kπ-π/2≤2x+π/6≤2kπ+π/2
那么kπ-π/3≤x≤kπ+π/6
即单调递增区间为[kπ-π/3,kπ+π/6] (k∈Z)

y=(1/2)cos²x+(√3/2)sinxcosx
=(1/2)[1+cos(2x)]/2 +(√3/4)sin(2x)
=(√3/4)sin(2x)+(1/4)cos(2x) +1/4
=(1/2)[(√3/2)sin(2x)+(1/2)cos(2x)] +1/4
=(1/2)sin(2x+π/6) +1/4
2kπ-π/2≤2x+π/6≤2...

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y=(1/2)cos²x+(√3/2)sinxcosx
=(1/2)[1+cos(2x)]/2 +(√3/4)sin(2x)
=(√3/4)sin(2x)+(1/4)cos(2x) +1/4
=(1/2)[(√3/2)sin(2x)+(1/2)cos(2x)] +1/4
=(1/2)sin(2x+π/6) +1/4
2kπ-π/2≤2x+π/6≤2kπ+π/2 (k∈Z)
kπ -π/3≤x≤kπ+π/6 (k∈Z)
函数的递增区间为[kπ-π/3，kπ+π/6] (k∈Z)

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