已知函数y=1/2cos^2x+sinxcosx+3/2sin^2x(x属于R）大神们帮个忙!哭求!

已知函数y=1/2cos^2x+sinxcosx+3/2sin^2x(x属于R）大神们帮个忙!哭求!
已知函数y=1/2cos^2x+sinxcosx+3/2sin^2x(x属于R）
求1）函数的最小正周期；2）函数的最大值、最小值；3）函数的单调区间

y=(1/2)cos²x+sinxcosx+(3/2)sin²x
=(1/2)(sin²x+cos²x)+(1/2)(2sinxcosx)+sin²x
=1/2 +(1/2)sin(2x)+(1/2)[1-cos(2x)]
=(1/2)[sin(2x)-cos(2x)] +1
=(√2/2)[(√2/2)sin(2x)-(√2/2)cos(2x)] +1
=(√2/2)sin(2x -π/4)+1
最小正周期T=2π/2=π
sin(2x- π/4)=1时,y有最大值ymax=√2/2 +1
sin(2x- π/4)=-1时,y有最小值yin=1- √2/2
2kπ-π/2≤2x-π/4≤2kπ+π/2 (k∈Z)时,函数单调递增,此时kπ-π/8≤x≤kπ+3π/8 (k∈Z)
2kπ+π/2≤2x-π/4≤2kπ+3π/2 (k∈Z)时,函数单调递减,此时kπ+3π/8≤x≤kπ+7π/8 (k∈Z)
函数的单调递增区间为[kπ-π/8,kπ+3π/8] (k∈Z),单调递减区间为[kπ+3π/8,kπ+7π/8] (k∈Z)