陈年老酒
春芽
共回答了16个问题采纳率:93.8% 举报
f(x)=sin(x/2)cos(x/2)+cos^2(x/2)-1.
=(1/2)sinx+(1+cosx)/2-1.
=(1/2)sinx+(1/2)cosx-1/2.
=(1/2)(sinx+cosx)-1/2.
∴f(x)=(√2/2)sin(x+π/4)-1/2.
f(x)的最小正周期T=2π;
∵sinx的递减区间是x∈[2kπ+π/2,2kπ+3π/2],k∈Z.
∴sin(x+π/4)的递减区间是(x+π/4)∈[2kπ+3π/4,2kπ+7π/4],k∈Z.
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